Computational models of plant development and form

The hidden diversity of vascular patterns in flower heads

Vascular systems are intimately related to the shape and spatial arrangement of the plant organs they support. We investigate the largely unexplored association between spiral phyllotaxis and the vascular system in Asteraceae flower heads. We imaged heads of eight species using synchrotron-based X-ray micro-computed tomography and applied original virtual reality and haptic software to explore head vasculature in three dimensions. We then constructed a computational model to infer a plausible patterning mechanism. The vascular system in the head of the model plant Gerbera hybrida is qualitatively different from those of Bellis perennis and Helianthus annuus, characterized previously. Cirsium vulgare, Craspedia globosa, Echinacea purpurea, Echinops bannaticus, and Tanacetum vulgare represent variants of the Bellis and Helianthus systems. In each species, the layout of the main strands is stereotypical, but details vary. The observed vascular patterns can be generated by a common computational model with different parameter values. In spite of the observed differences of vascular systems in heads, they may be produced by a conserved mechanism. The diversity and irregularities of vasculature stand in contrast with the relative uniformity and regularity of phyllotactic patterns, confirming that phyllotaxis in heads is not driven by the vasculature.

Tapping into the plasticity of plant architecture for increased stress resilience

Plant architecture develops post-embryonically and emerges from a dialogue between the developmental signals and environmental cues. Length and branching of the vegetative and reproductive tissues were the focus of improvement of plant performance from the early days of plant breeding. Current breeding priorities are changing, as we need to prioritize plant productivity under increasingly challenging environmental conditions. While it has been widely recognized that plant architecture changes in response to the environment, its contribution to plant productivity in the changing climate remains to be fully explored. This review will summarize prior discoveries of genetic control of plant architecture traits and their effect on plant performance under environmental stress. We review new tools in phenotyping that will guide future discoveries of genes contributing to plant architecture, its plasticity, and its contributions to stress resilience. Subsequently, we provide a perspective into how integrating the study of new species, modern phenotyping techniques, and modeling can lead to discovering new genetic targets underlying the plasticity of plant architecture and stress resilience. Altogether, this review provides a new perspective on the plasticity of plant architecture and how it can be harnessed for increased performance under environmental stress.

Computer models of cell polarity establishment in plants

Plant development is a complex task, and many processes involve changes in the asymmetric subcellular distribution of cell components that strongly depend on cell polarity. Cell polarity regulates anisotropic growth and polar localization of membrane proteins and helps to identify the cell's position relative to its neighbors within an organ. Cell polarity is critical in a variety of plant developmental processes, including embryogenesis, cell division, and response to external stimuli. The most conspicuous downstream effect of cell polarity is the polar transport of the phytohormone auxin, which is the only known hormone transported in a polar fashion in and out of cells by specialized exporters and importers. The biological processes behind the establishment of cell polarity are still unknown, and researchers have proposed several models that have been tested using computer simulations. The evolution of computer models has progressed in tandem with scientific discoveries, which have highlighted the importance of genetic, chemical, and mechanical input in determining cell polarity and regulating polarity-dependent processes such as anisotropic growth, protein subcellular localization, and the development of organ shapes. The purpose of this review is to provide a comprehensive overview of the current understanding of computer models of cell polarity establishment in plants, focusing on the molecular and cellular mechanisms, the proteins involved, and the current state of the field.

Hormonal control of medial-lateral growth and vein formation in the maize leaf

Parallel veins are characteristic of monocots, including grasses (Poaceae). Therefore, how parallel veins develop as the leaf grows in the medial-lateral (ML) dimension is a key question in grass leaf development. Using fluorescent protein reporters, we mapped auxin, cytokinin (CK), and gibberellic acid (GA) response patterns in maize (Zea mays) leaf primordia. We further defined the roles of these hormones in ML growth and vein formation through combinatorial genetic analyses and measurement of hormone concentrations. We discovered a novel pattern of auxin response in the adaxial protoderm that we hypothesize has important implications for the orderly formation of 3° veins early in leaf development. In addition, we found an auxin transport and response pattern in the margins that correlate with the transition from ML to proximal-distal growth. We present evidence that auxin efflux precedes CK response in procambial strand development. We also determined that GA plays an early role in the shoot apical meristem as well as a later role in the primordium to restrict ML growth. We propose an integrative model whereby auxin regulates ML growth and vein formation in the maize leaf through control of GA and CK.

The mechanics of plant morphogenesis

Understanding the mechanism by which patterned gene activity leads to mechanical deformation of cells and tissues to create complex forms is a major challenge for developmental biology. Plants offer advantages for addressing this problem because their cells do not migrate or rearrange during morphogenesis, which simplifies analysis. We synthesize results from experimental analysis and computational modeling to show how mechanical interactions between cellulose fibers translate through wall, cell, and tissue levels to generate complex plant tissue shapes. Genes can modify mechanical properties and stresses at each level, though the values and pattern of stresses differ from one level to the next. The dynamic cellulose network provides elastic resistance to deformation while allowing growth through fiber sliding, which enables morphogenesis while maintaining mechanical strength.

Fourteen Stations of Auxin

Auxin has always been at the forefront of research in plant physiology and development. Since the earliest contemplations by Julius von Sachs and Charles Darwin, more than a century-long struggle has been waged to understand its function. This largely reflects the failures, successes, and inevitable progress in the entire field of plant signaling and development. Here I present 14 stations on our long and sometimes mystical journey to understand auxin. These highlights were selected to give a flavor of the field and to show the scope and limits of our current knowledge. A special focus is put on features that make auxin unique among phytohormones, such as its dynamic, directional transport network, which integrates external and internal signals, including self-organizing feedback. Accented are persistent mysteries and controversies. The unexpected discoveries related to rapid auxin responses and growth regulation recently disturbed our contentment regarding understanding of the auxin signaling mechanism. These new revelations, along with advances in technology, usher us into a new, exciting era in auxin research.

The shaping of plant axes and crowns through tropisms and elasticity: an example of morphogenetic plasticity beyond the shoot apical meristem

Shoot morphogenetic plasticity is crucial to the adaptation of plants to their fluctuating environments. Major insights into shoot morphogenesis have been compiled studying meristems, especially the shoot apical meristem (SAM), through a methodological effort in multiscale systems biology and biophysics. However, morphogenesis at the SAM is robust to environmental changes. Plasticity emerges later on during post-SAM development. The purpose of this review is to show that multiscale systems biology and biophysics is insightful for the shaping of the whole plant as well. More specifically, we review the shaping of axes and crowns through tropisms and elasticity, combining the recent advances in morphogenetic control using physical cues and by genes. We focus mostly on land angiosperms, but with growth habits ranging from small herbs to big trees. We show that generic (universal) morphogenetic processes have been identified, revealing feedforward and feedback effects of global shape on the local morphogenetic process. In parallel, major advances have been made in the analysis of the major genes involved in shaping axes and crowns, revealing conserved genic networks among angiosperms. Then, we show that these two approaches are now starting to converge, revealing exciting perspectives.

3D modeling and reconstruction of plants and trees: A cross-cutting review across computer graphics, vision, and plant phenotyping

This paper reviews the past and current trends of three-dimensional (3D) modeling and reconstruction of plants and trees. These topics have been studied in multiple research fields, including computer vision, graphics, plant phenotyping, and forestry. This paper, therefore, provides a cross-cutting review. Representations of plant shape and structure are first summarized, where every method for plant modeling and reconstruction is based on a shape/structure representation. The methods were then categorized into 1) creating non-existent plants (modeling) and 2) creating models from real-world plants (reconstruction). This paper also discusses the limitations of current methods and possible future directions.

Computational Models of Auxin-Driven Patterning in Shoots

Auxin regulates many aspects of plant development and behavior, including the initiation of new outgrowth, patterning of vascular systems, control of branching, and responses to the environment. Computational models have complemented experimental studies of these processes. We review these models from two perspectives. First, we consider cellular and tissue-level models of interaction between auxin and its transporters in shoots. These models form a coherent body of results exploring different hypotheses pertinent to the patterning of new outgrowth and vascular strands. Second, we consider models operating at the level of plant organs and entire plants. We highlight techniques used to reduce the complexity of these models, which provide a path to capturing the essence of studied phenomena while running simulations efficiently.

Shaping the Organ: A Biologist Guide to Quantitative Models of Plant Morphogenesis

Organ morphogenesis is the process of shape acquisition initiated with a small reservoir of undifferentiated cells. In plants, morphogenesis is a complex endeavor that comprises a large number of interacting elements, including mechanical stimuli, biochemical signaling, and genetic prerequisites. Because of the large body of data being produced by modern laboratories, solving this complexity requires the application of computational techniques and analyses. In the last two decades, computational models combined with wet-lab experiments have advanced our understanding of plant organ morphogenesis. Here, we provide a comprehensive review of the most important achievements in the field of computational plant morphodynamics. We present a brief history from the earliest attempts to describe plant forms using algorithmic pattern generation to the evolution of quantitative cell-based models fueled by increasing computational power. We then provide an overview of the most common types of "digital plant" paradigms, and demonstrate how models benefit from diverse techniques used to describe cell growth mechanics. Finally, we highlight the development of computational frameworks designed to resolve organ shape complexity through integration of mechanical, biochemical, and genetic cues into a quantitative standardized and user-friendly environment.

Leaf Shape Diversity: From Genetic Modules to Computational Models

Plant leaves display considerable variation in shape. Here, we introduce key aspects of leaf development, focusing on the morphogenetic basis of leaf shape diversity. We discuss the importance of the genetic control of the amount, duration, and direction of cellular growth for the emergence of leaf form. We highlight how the combined use of live imaging and computational frameworks can help conceptualize how regulated cellular growth is translated into different leaf shapes. In particular, we focus on the morphogenetic differences between simple and complex leaves and how carnivorous plants form three-dimensional insect traps. We discuss how evolution has shaped leaf diversity in the case of complex leaves, by tinkering with organ-wide growth and local growth repression, and in carnivorous plants, by modifying the relative growth of the lower and upper sides of the leaf primordium to create insect-digesting traps.

Overcoming the Challenges to Enhancing Experimental Plant Biology With Computational Modeling

The study of complex biological systems necessitates computational modeling approaches that are currently underutilized in plant biology. Many plant biologists have trouble identifying or adopting modeling methods to their research, particularly mechanistic mathematical modeling. Here we address challenges that limit the use of computational modeling methods, particularly mechanistic mathematical modeling. We divide computational modeling techniques into either pattern models (e.g., bioinformatics, machine learning, or morphology) or mechanistic mathematical models (e.g., biochemical reactions, biophysics, or population models), which both contribute to plant biology research at different scales to answer different research questions. We present arguments and recommendations for the increased adoption of modeling by plant biologists interested in incorporating more modeling into their research programs. As some researchers find math and quantitative methods to be an obstacle to modeling, we provide suggestions for easy-to-use tools for non-specialists and for collaboration with specialists. This may especially be the case for mechanistic mathematical modeling, and we spend some extra time discussing this. Through a more thorough appreciation and awareness of the power of different kinds of modeling in plant biology, we hope to facilitate interdisciplinary, transformative research.

EvoDevo: Past and Future of Continuum and Process Plant Morphology

Plants and animals are both important for studies in evolutionary developmental biology (EvoDevo). Plant morphology as a valuable discipline of EvoDevo is set for a paradigm shift. Process thinking and the continuum approach in plant morphology allow us to perceive and interpret growing plants as combinations of developmental processes rather than as assemblages of structural units (“organs”) such as roots, stems, leaves, and flowers. These dynamic philosophical perspectives were already favored by botanists and philosophers such as Agnes Arber (1879–1960) and Rolf Sattler (*1936). The acceptance of growing plants as dynamic continua inspires EvoDevo scientists such as developmental geneticists and evolutionary biologists to move towards a more holistic understanding of plants in time and space. This review will appeal to many young scientists in the plant development research fields. It covers a wide range of relevant publications from the past to present.

An overview of agent-based models in plant biology and ecology

Agent-based modelling (ABM) has become an established methodology in many areas of biology, ranging from the cellular to the ecological population and community levels. In plant science, two different scales have predominated in their use of ABM. One is the scale of populations and communities, through the modelling of collections of agents representing individual plants, interacting with each other and with the environment. The other is the scale of the individual plant, through the modelling, by functional-structural plant models (FSPMs), of agents representing plant building blocks, or metamers, to describe the development of plant architecture and functions within individual plants. The purpose of this review is to show key results and parallels in ABM for growth, mortality, carbon allocation, competition and reproduction across the scales from the plant organ to populations and communities on a range of spatial scales to the whole landscape. Several areas of application of ABMs are reviewed, showing that some issues are addressed by both population-level ABMs and FSPMs. Continued increase in the relevance of ABM to environmental science and management will be helped by greater integration of ABMs across these two scales.

Field-based mechanical phenotyping of cereal crops to assess lodging resistance

Plant mechanical failure, also known as lodging, is the cause of significant and unpredictable yield losses in cereal crops. Lodging occurs in two distinct failure modes-stalk lodging and root lodging. Despite the prevalence and detrimental impact of lodging on crop yields, there is little consensus on how to phenotype plants in the field for lodging resistance and thus breed for mechanically resilient plants. This review provides an overview of field-based mechanical testing approaches to assess stalk and root lodging resistance. These approaches are placed in the context of future perspectives. Best practices and recommendations for acquiring field-based mechanical phenotypes of plants are also presented.

Vein patterning by tissue-specific auxin transport

Unlike in animals, in plants, vein patterning does not rely on direct cell-cell interaction and cell migration; instead, it depends on the transport of the plant hormone auxin, which in turn depends on the activity of the PIN-FORMED1 (PIN1) auxin transporter. The current hypotheses of vein patterning by auxin transport propose that, in the epidermis of the developing leaf, PIN1-mediated auxin transport converges to peaks of auxin level. From those convergence points of epidermal PIN1 polarity, auxin would be transported in the inner tissues where it would give rise to major veins. Here, we have tested predictions of this hypothesis and have found them unsupported: epidermal PIN1 expression is neither required nor sufficient for auxin transport-dependent vein patterning, whereas inner-tissue PIN1 expression turns out to be both required and sufficient for auxin transport-dependent vein patterning. Our results refute all vein patterning hypotheses based on auxin transport from the epidermis and suggest alternatives for future tests.

Response of Beech (Fagus sylvatica L.) Trees to Competition—New Insights from Using Fractal Analysis

Individual tree architecture and the composition of tree species play a vital role for many ecosystem functions and services provided by a forest, such as timber value, habitat diversity, and ecosystem resilience. However, knowledge is limited when it comes to understanding how tree architecture changes in response to competition. Using 3D-laser scanning data from the German Biodiversity Exploratories, we investigated the detailed three-dimensional architecture of 24 beech (Fagus sylvatica L.) trees that grew under different levels of competition pressure. We created detailed quantitative structure models (QSMs) for all study trees to describe their branching architecture. Furthermore, structural complexity and architectural self-similarity were measured using the box-dimension approach from fractal analysis. Relating these measures to the strength of competition, the trees are exposed to reveal strong responses for a wide range of tree architectural measures indicating that competition strongly changes the branching architecture of trees. The strongest response to competition (rho = −0.78) was observed for a new measure introduced here, the intercept of the regression used to determine the box-dimension. This measure was discovered as an integrating descriptor of the size of the complexity-bearing part of the tree, namely the crown, and proven to be even more sensitive to competition than the box-dimension itself. Future studies may use fractal analysis to investigate and quantify the response of tree individuals to competition.

The Wiring of Intelligence

The positive manifold of intelligence has fascinated generations of scholars in human ability. In the past century, various formal explanations have been proposed, including the dominant g factor, the revived sampling theory, and the recent multiplier effect model and mutualism model. In this article, we propose a novel idiographic explanation. We formally conceptualize intelligence as evolving networks in which new facts and procedures are wired together during development. The static model, an extension of the Fortuin-Kasteleyn model, provides a parsimonious explanation of the positive manifold and intelligence's hierarchical factor structure. We show how it can explain the Matthew effect across developmental stages. Finally, we introduce a method for studying growth dynamics. Our truly idiographic approach offers a new view on a century-old construct and ultimately allows the fields of human ability and human learning to coalesce.

Helios: A Scalable 3D Plant and Environmental Biophysical Modeling Framework

This article presents an overview of Helios, a new three-dimensional (3D) plant and environmental modeling framework. Helios is a model coupling framework designed to provide maximum flexibility in integrating and running arbitrary 3D environmental system models. Users interact with Helios through a well-documented open-source C++ API. Version 1.0 comes with model plug-ins for radiation transport, the surface energy balance, stomatal conductance, photosynthesis, solar position, and procedural tree generation. Additional plug-ins are also available for visualizing model geometry and data and for processing and integrating LiDAR scanning data. Many of the plug-ins perform calculations on the graphics processing unit, which allows for efficient simulation of very large domains with high detail. An example modeling study is presented in which leaf-level heterogeneity in water usage and photosynthesis of an orchard is examined to understand how this leaf-scale variability contributes to whole-tree and -canopy fluxes.

Constructing living buildings: a review of relevant technologies for a novel application of biohybrid robotics

Biohybrid robotics takes an engineering approach to the expansion and exploitation of biological behaviours for application to automated tasks. Here, we identify the construction of living buildings and infrastructure as a high-potential application domain for biohybrid robotics, and review technological advances relevant to its future development. Construction, civil infrastructure maintenance and building occupancy in the last decades have comprised a major portion of economic production, energy consumption and carbon emissions. Integrating biological organisms into automated construction tasks and permanent building components therefore has high potential for impact. Live materials can provide several advantages over standard synthetic construction materials, including self-repair of damage, increase rather than degradation of structural performance over time, resilience to corrosive environments, support of biodiversity, and mitigation of urban heat islands. Here, we review relevant technologies, which are currently disparate. They span robotics, self-organizing systems, artificial life, construction automation, structural engineering, architecture, bioengineering, biomaterials, and molecular and cellular biology. In these disciplines, developments relevant to biohybrid construction and living buildings are in the early stages, and typically are not exchanged between disciplines. We, therefore, consider this review useful to the future development of biohybrid engineering for this highly interdisciplinary application.

Formal description of plant morphogenesis

Plant morphogenesis may be characterized by complex feedback mechanisms between signals specifying growth and by the growth of the plant body itself. Comprehension of such feedback mechanisms is an ongoing research task and can be aided with formal descriptions of morphogenesis. In this review, we present a number of established mathematical paradigms that are useful to the formal representation of plant shape, and of biomechanical and biochemical signaling. Specifically, we discuss work from a range of research areas including plant biology, material sciences, fluid dynamics, and computer graphics. Treating plants as organized systems of information processing allows us to compare these different mathematical methods in terms of their expressive power of biological hypotheses. This is an attempt to bring together a large number of computational modeling concepts and make them accessible to the analytical as well as empirical student of plant morphogenesis.

Volumetric finite-element modelling of biological growth

Differential growth is the driver of tissue morphogenesis in plants, and also plays a fundamental role in animal development. Although the contributions of growth to shape change have been captured through modelling tissue sheets or isotropic volumes, a framework for modelling both isotropic and anisotropic volumetric growth in three dimensions over large changes in size and shape has been lacking. Here, we describe an approach based on finite-element modelling of continuous volumetric structures, and apply it to a range of forms and growth patterns, providing mathematical validation for examples that admit analytic solution. We show that a major difference between sheet and bulk tissues is that the growth of bulk tissue is more constrained, reducing the possibility of tissue conflict resolution through deformations such as buckling. Tissue sheets or cylinders may be generated from bulk shapes through anisotropic specified growth, oriented by a polarity field. A second polarity field, orthogonal to the first, allows sheets with varying lengths and widths to be generated, as illustrated by the wide range of leaf shapes observed in nature. The framework we describe thus provides a key tool for developing hypotheses for plant morphogenesis and is also applicable to other tissues that deform through differential growth or contraction.

Theoretical models for branch formation in plants

Various branch architectures are observed in living organisms including plants. Branch formation has traditionally been an area of interest in the field of developmental biology, and theoretical approaches are now commonly used to understand the complex mechanisms involved. In this review article, we provide an overview of theoretical approaches including mathematical models and computer simulations for studying plant branch formation. These approaches cover a wide range of topics. In particular, we focus on the importance of positional information in branch formation, which has been especially revealed by theoretical research in plants including computations of developmental processes.

Practical steps to digital organism models, from laboratory model species to 'Crops in silico

A recent initiative named 'Crops in silico' proposes that multi-scale models 'have the potential to fill in missing mechanistic details and generate new hypotheses to prioritize directed engineering efforts' in plant science, particularly directed to crop species. To that end, the group called for 'a paradigm shift in plant modelling, from largely isolated efforts to a connected community'. 'Wet' (experimental) research has been especially productive in plant science, since the adoption of Arabidopsis thaliana as a laboratory model species allowed the emergence of an Arabidopsis research community. Parts of this community invested in 'dry' (theoretical) research, under the rubric of Systems Biology. Our past research combined concepts from Systems Biology and crop modelling. Here we outline the approaches that seem most relevant to connected, 'digital organism' initiatives. We illustrate the scale of experimental research required, by collecting the kinetic parameter values that are required for a quantitative, dynamic model of a gene regulatory network. By comparison with the Systems Biology Markup Language (SBML) community, we note computational resources and community structures that will help to realize the potential for plant Systems Biology to connect with a broader crop science community.

Understanding and optimizing species mixtures using functional-structural plant modelling

Plant species mixtures improve productivity over monocultures by exploiting species complementarities for resource capture in time and space. Complementarity results in part from competition avoidance responses that maximize resource capture and growth of individual plants. Individual organs accommodate to local resource levels, e.g. with regard to nitrogen content and photosynthetic capacity or by size (e.g. shade avoidance). As a result, the resource acquisition in time and space is improved and performance of the community as a whole is increased. Modelling is needed to unravel the primary drivers and subsequent dynamics of complementary growth responses in mixtures. Here, we advocate using functional-structural plant (FSP) modelling to analyse the functioning of plant mixtures. In FSP modelling, crop performance is a result of the behaviour of the individual plants interacting through competitive and complementary resource acquisition. FSP models can integrate the interactions between structural and physiological plant responses to the local resource availability and strength of competition, which drive resource capture and growth of individuals in species mixtures. FSP models have the potential to accelerate mixed-species plant research, and thus support the development of knowledge that is needed to promote the use of mixtures towards sustainably increasing crop yields at acceptable input levels.

Investigation of complex canopies with a functional-structural plant model as exemplified by leaf inclination effect on the functioning of pure and mixed stands of wheat during grain filling

BACKGROUND AND AIMS

Because functional-structural plant models (FSPMs) take plant architecture explicitly into consideration, they constitute a promising approach for unravelling plant-plant interactions in complex canopies. However, existing FSPMs mainly address competition for light. The aim of the present work was to develop a comprehensive FSPM accounting for the interactions between plant architecture, environmental factors and the metabolism of carbon (C) and nitrogen (N).

METHODS

We developed an original FSPM by coupling models of (1) 3-D wheat architecture, (2) light distribution within canopies and (3) C and N metabolism. Model behaviour was evaluated by simulating the functioning of theoretical canopies consisting of wheat plants of contrasting leaf inclination, arranged in pure and mixed stands and considering four culm densities and three sky conditions.

KEY RESULTS

As an emergent property of the detailed description of metabolism, the model predicted a linear relationship between absorbed light and C assimilation, and a curvilinear relationship between grain mass and C assimilation, applying to both pure stands and each component of mixtures. Over the whole post-anthesis period, planophile plants tended to absorb more light than erectophile plants, resulting in a slightly higher grain mass. This difference was enhanced at low plant density and in mixtures, where the erectophile behaviour resulted in a loss of competitiveness.

CONCLUSION

The present work demonstrates that FSPMs provide a framework allowing the analysis of complex canopies such as studying the impact of particular plant traits, which would hardly be feasible experimentally. The present FSPM can help in interpreting complex interactions by providing access to critical variables such as resource acquisition and allocation, internal metabolic concentrations, leaf life span and grain filling. Simulations were based on canopies identically initialized at flowering; extending the model to the whole cycle is thus required so that all consequences of a trait can be evaluated.

Development of a Peanut Canopy Measurement System Using a Ground-Based LiDAR Sensor

Plant architecture characteristics contribute significantly to the microclimate within peanut canopies, affecting weed suppression as well as incidence and severity of foliar and soil-borne diseases. However, plant canopy architecture is difficult to measure and describe quantitatively. In this study, a ground-based LiDAR sensor was used to scan rows of peanut plants in the field, and a data processing and analysis algorithm was developed to extract feature indices to describe the peanut canopy architecture. A data acquisition platform was constructed to carry the ground-based LiDAR and an RGB camera during field tests. An experimental field was established with three peanut cultivars at Oklahoma State University's Caddo Research Station in Fort Cobb, OK in May and the data collections were conducted once each month from July to September 2015. The ground-based LiDAR used for this research was a line-scan laser scanner with a scan-angle of 100°, an angle resolution of 0.25°, and a scanning speed of 53 ms. The collected line-scanned data were processed using the developed image processing algorithm. The canopy height, width, and shape/density were evaluated. Euler number, entropy, cluster count, and mean number of connected objects were extracted from the image and used to describe the shape of the peanut canopies. The three peanut cultivars were then classified using the shape features and indices. A high correlation was also observed between the LiDAR and ground-truth measurements for plant height. This approach should be useful for phenotyping peanut germplasm for canopy architecture.

Cell geometry determines symmetric and asymmetric division plane selection in Arabidopsis early embryos

Plant tissue architecture and organ morphogenesis rely on the proper orientation of cell divisions. Previous attempts to predict division planes from cell geometry in plants mostly focused on 2D symmetric divisions. Using the stereotyped division patterns of Arabidopsis thaliana early embryogenesis, we investigated geometrical principles underlying plane selection in symmetric and in asymmetric divisions within complex 3D cell shapes. Introducing a 3D computational model of cell division, we show that area minimization constrained on passing through the cell centroid predicts observed divisions. Our results suggest that the positioning of division planes ensues from cell geometry and gives rise to spatially organized cell types with stereotyped shapes, thus underlining the role of self-organization in the developing architecture of the embryo. Our data further suggested the rule could be interpreted as surface minimization constrained by the nucleus position, which was validated using live imaging of cell divisions in the stomatal cell lineage.

The proper positioning of division planes is key for correct development and morphogenesis of organs, in particular in plants were cellular walls prevent cell rearrangements. Elucidating how division planes are selected is therefore essential to decipher the cellular bases of plant morphogenesis. Previous attempts to identify geometrical rules relating cell shape and division plane positioning in plants mostly focused on symmetric divisions in tissues reduced to 2D geometries. Here, we combined 3D quantitative image analysis and a new 3D cell division model to evaluate the existence of geometrical rules in asymmetrical and symmetrical divisions of complex cell shapes. We show that in the early embryo of the model plant Arabidopsis thaliana, which presents stereotyped but complex cell division patterns, a single geometrical rule (area minimization constrained on passing through the cell centroid) recapitulates the complete sequence of division events. This new rule, valid for both symmetrical and asymmetrical divisions, generalizes previously proposed cell division rules and can be interpreted based on the dynamics of the cytoskeleton and on the positioning of the nucleus, a hypothesis that we validated using leaf cell division patterns. This work highlights the importance of self-organization in plant early morphogenesis and the emergence of robust cellular organizations based on geometrical feedback loops between cell geometry and division plane selection.

Molecular cartography of leaf development - role of transcription factors

Organ elaboration in plants occurs almost exclusively by an increase in cell number and size. Leaves, the planar lateral appendages of plants, are no exception. Forward and reverse genetic approaches have identified several genes whose role in leaf morphogenesis has been inferred from their primary effect on cell number and size, thereby distinguishing them as either promoters or inhibitors of cell proliferation and expansion. While such classification is useful in studying size control, a similar link between genes and shape generation is poorly understood. Computational modelling can provide a conceptual framework to re-evaluate the known genetic information and assign specific morphogenetic roles to the transcription factor-encoding genes. Here we discuss recent advances in our understanding of the roles of transcription factors in the planar growth of leaf lamina in two orthogonal dimensions.

Leaf development and evolution

Plant leaves are differentiated organs that arise sequentially from a population of pluripotent stem cells at the shoot apical meristem (SAM). There is substantial diversity in leaf shape, much of which depends on the size and arrangement of outgrowths at the leaf margin. These outgrowths are generated by a patterning mechanism similar to the phyllotactic processes producing organs at the SAM, which involves the transcription factors CUP-SHAPED COTYLEDON and the phytohormone auxin. In the leaf, this patterning mechanism creates sequential protrusions and indentations along the margin. The size, shape, and distribution of these protrusions also depend on the overall growth of the leaf lamina. Globally, growth is regulated by a complex genetic network controlling the distribution of cell proliferation and the timing of differentiation. Evolutionary changes in margin form arise from changes in two different classes of homeobox genes that modify the outcome of marginal patterning in diverse ways, and are under intense investigation.

Cell-Based Model of the Generation and Maintenance of the Shape and Structure of the Multilayered Shoot Apical Meristem of Arabidopsis thaliana

One of the central problems in animal and plant developmental biology is deciphering how chemical and mechanical signals interact within a tissue to produce organs of defined size, shape, and function. Cell walls in plants impose a unique constraint on cell expansion since cells are under turgor pressure and do not move relative to one another. Cell wall extensibility and constantly changing distribution of stress on the wall are mechanical properties that vary between individual cells and contribute to rates of expansion and orientation of cell division. How exactly cell wall mechanical properties influence cell behavior is still largely unknown. To address this problem, a novel, subcellular element computational model of growth of stem cells within the multilayered shoot apical meristem (SAM) of Arabidopsis thaliana is developed and calibrated using experimental data. Novel features of the model include separate, detailed descriptions of cell wall extensibility and mechanical stiffness, deformation of the middle lamella, and increase in cytoplasmic pressure generating internal turgor pressure. The model is used to test novel hypothesized mechanisms of formation of the shape and structure of the growing, multilayered SAM based on WUS concentration of individual cells controlling cell growth rates and layer-dependent anisotropic mechanical properties of subcellular components of individual cells determining anisotropic cell expansion directions. Model simulations also provide a detailed prediction of distribution of stresses in the growing tissue which can be tested in future experiments.

Algorithm for a particle-based growth model for plant tissues

We have developed an algorithm for a particle-based model for the growth of plant tissues in three dimensions in which each cell is represented by a single particle, and connecting cell walls are represented as permanent bonds between particles. A sample of plant tissue is represented by a fixed network of bonded particles. If, and only if a cell divides, this network is updated locally. The update algorithm is implemented in a model where cell growth and division gives rise to forces between the cells, which are relaxed in steepest descent minimization. The same forces generate a pressure inside the cells, which moderates growth. The local nature of the algorithm makes it efficient computationally, so the model can deal with a large number of cells. We used the model to study the growth of plant tissues for a variety of model parameters, to show the viability of the algorithm.

Similar bowtie structures and distinct largest strong components are identified in the transcriptional regulatory networks of Arabidopsis thaliana during photomorphogenesis and heat shock

Photomorphogenesis and heat shock are critical biological processes of plants. A recent research constructed the transcriptional regulatory networks (TRNs) of Arabidopsis thaliana during these processes using DNase-seq. In this study, by strong decomposition, we revealed that each of these TRNs can be represented as a similar bowtie structure with only one non-trivial and distinct strong component. We further identified distinct patterns of variation of a few light-related genes in these bowtie structures during photomorphogenesis. These results suggest that bowtie structure may be a common property of TRNs of plants, and distinct variation patterns of genes in bowtie structures of TRNs during biological processes may reflect distinct functions. Overall, our study provides an insight into the molecular mechanisms underlying photomorphogenesis and heat shock, and emphasizes the necessity to investigate the strong connectivity structures while studying TRNs.

Flower-like heads from flower-like meristems: pseudanthium development in Davidia involucrata (Nyssaceae)

Flower-like inflorescences (pseudanthia) have fascinated botanists for a long time. They are explained as condensed inflorescences implying that the pseudanthium develops from an inflorescence meristem (IM). However, recent developmental studies identified a new form of reproductive meristem, the floral unit meristem (FUM). It differs from IMs by lacking acropetal growth and shares fractionation, expansion and autonomous space filling with flower meristems (FM). The similarity among FUMs and FMs raises the question how far flower-like heads originate from flower-like meristems. In the present paper, pseudanthium development in Davidia involucrata is investigated using scanning electron microscopy. D. involucrata has pincushion-shaped heads composed of densely aggregated, perianthless flowers and associated with two large showy bracts. Early developmental stages show a huge naked FUM. The FMs appear almost simultaneously and lack subtending bracts. With ongoing FUM expansion new space is generated which is immediately used by further FM fractionation. The heads have only staminate flowers or are andromonoecious with staminate and a single perfect flower in oblique position. All FMs lack perianth structures and fractionate a variable number of stamen primordia. The perfect FM is much larger than the staminate FMs and forms a syncarpous gynoecium with inferior ovary. Pseudanthium development in D. involucrata confirms the morphogenetic similarity to FMs as to acropetal growth limitation, meristem expansion and fractionation. It thus should not be interpreted as a condensed inflorescence, but as a flower equivalent. Furthermore as the FUM develops inside a bud, its development is considered to be influenced by mechanical pressure. The oblique position of the perfect flower, the developmental delay of the proximal flowers, and the variable number of stamens which were observed in the pseudanthium development, can be caused by mechanical pressure. Next to the Asteraceae, D. involucrata offers a further example of a pseudanthium originating from a FUM. More knowledge on FUMs is still needed to understand diversification and evolution of flower-like inflorescences.

Computational botany: advancing plant science through functional–structural plant modelling

The need to integrate the ever-expanding body of knowledge in the plant sciences has led to the development of sophisticated modelling approaches. This special issue focuses on functional–structural plant (FSP) models, which are the result of cross-fertilization between the domains of plant science, computer science and mathematics. FSP models simulate growth and morphology of individual plants that interact with their environment, from which complex plant community properties emerge. FSP models can be used for a broad range of research questions across disciplines related to plant science. This special issue presents the latest developments in FSP modelling, including the novel incorporation of plant ecophysiological concepts and the application of FSP models to address new scientific questions. Additionally, it illustrates the breadth of model evaluation approaches that are performed. FSP modelling is a very active domain of plant research which brings together a wide range of scientific disciplines. It offers the opportunity to address questions in complex plant systems that cannot be addressed by empirical approaches alone, including questions on fundamental concepts related to plant development such as regulation of morphogenesis, as well as on applied concepts such as the relationship between crop performance and plant competition for resources.

The use of plant models in deep learning: an application to leaf counting in rosette plants

Deep learning presents many opportunities for image-based plant phenotyping. Here we consider the capability of deep convolutional neural networks to perform the leaf counting task. Deep learning techniques typically require large and diverse datasets to learn generalizable models without providing a priori an engineered algorithm for performing the task. This requirement is challenging, however, for applications in the plant phenotyping field, where available datasets are often small and the costs associated with generating new data are high. In this work we propose a new method for augmenting plant phenotyping datasets using rendered images of synthetic plants. We demonstrate that the use of high-quality 3D synthetic plants to augment a dataset can improve performance on the leaf counting task. We also show that the ability of the model to generate an arbitrary distribution of phenotypes mitigates the problem of dataset shift when training and testing on different datasets. Finally, we show that real and synthetic plants are significantly interchangeable when training a neural network on the leaf counting task.

On genes and form

The mechanisms by which organisms acquire their sizes and shapes through growth was a major focus of D'Arcy Thompson's book On Growth and Form. By applying mathematical and physical principles to a range of biological forms, Thompson achieved fresh insights, such as the notion that diverse biological shapes could be related through simple deformations of a coordinate system. However, Thompson considered genetics to lie outside the scope of his work, even though genetics was a growing discipline at the time the book was published. Here, we review how recent advances in cell, developmental, evolutionary and computational biology allow Thompson's ideas to be integrated with genes and the processes they influence to provide a deeper understanding of growth and morphogenesis. We consider how genes interact with subcellular-, cellular- and tissue-level processes in plants to yield patterns of growth that underlie the developmental and evolutionary shape transformations Thompson so eloquently described.

A common developmental program can produce diverse leaf shapes

Eudicot leaves have astoundingly diverse shapes. The central problem addressed in this paper is the developmental origin of this diversity. To investigate this problem, we propose a computational model of leaf development that generalizes the largely conserved molecular program for the reference plants Arabidopsis thaliana, Cardamine hirsuta and Solanum lycopersicum. The model characterizes leaf development as a product of three interwoven processes: the patterning of serrations, lobes and/or leaflets on the leaf margin; the patterning of the vascular system; and the growth of the leaf blade spanning the main veins. The veins play a significant morphogenetic role as a local determinant of growth directions. We show that small variations of this model can produce diverse leaf shapes, from simple to lobed to compound. It is thus plausible that diverse shapes of eudicot leaves result from small variations of a common developmental program.

Understanding and engineering plant form

A plant's form is an important determinant of its fitness and economic value. Here, we review strategies for producing plants with altered forms. Historically, the process of changing a plant's form has been slow in agriculture, requiring iterative rounds of growth and selection. We discuss modern techniques for identifying genes involved in the development of plant form and tools that will be needed to effectively design and engineer plants with altered forms. Synthetic genetic circuits are highlighted for their potential to generate novel plant forms. We emphasize understanding development as a prerequisite to engineering and discuss the potential role of computer models in translating knowledge about single genes or pathways into a more comprehensive understanding of development.

Plant Science View on Biohybrid Development

Biohybrid consists of a living organism or cell and at least one engineered component. Designing robot-plant biohybrids is a great challenge: it requires interdisciplinary reconsideration of capabilities intimate specific to the biology of plants. Envisioned advances should improve agricultural/horticultural/social practice and could open new directions in utilization of plants by humans. Proper biohybrid cooperation depends upon effective communication. During evolution, plants developed many ways to communicate with each other, with animals, and with microorganisms. The most notable examples are: the use of phytohormones, rapid long-distance signaling, gravity, and light perception. These processes can now be intentionally re-shaped to establish plant-robot communication. In this article, we focus on plants physiological and molecular processes that could be used in bio-hybrids. We show phototropism and biomechanics as promising ways of effective communication, resulting in an alteration in plant architecture, and discuss the specifics of plants anatomy, physiology and development with regards to the bio-hybrids. Moreover, we discuss ways how robots could influence plants growth and development and present aims, ideas, and realized projects of plant-robot biohybrids.

High-Resolution Laser Scanning Reveals Plant Architectures that Reflect Universal Network Design Principles

Transport networks serve critical functions in biological and engineered systems, and yet their design requires trade-offs between competing objectives. Due to their sessile lifestyle, plants need to optimize their architecture to efficiently acquire and distribute resources while also minimizing costs in building infrastructure. To understand how plants resolve this design trade-off, we used high-precision three-dimensional laser scanning to map the architectures of tomato, tobacco, or sorghum plants grown in several environmental conditions and through multiple developmental time points, scanning in total 505 architectures from 37 plants. Using a graph-theoretic algorithm that we developed to evaluate design strategies, we find that plant architectures lie along the Pareto front between two simple length-based objectives-minimizing total branch length and minimizing nutrient transport distance-thereby conferring a selective fitness advantage for plant transport processes. The location along the Pareto front can distinguish among species and conditions, suggesting that during evolution, natural selection may employ common network design principles despite different optimization trade-offs.

Synthetic Botany

Plants are attractive platforms for synthetic biology and metabolic engineering. Plants' modular and plastic body plans, capacity for photosynthesis, extensive secondary metabolism, and agronomic systems for large-scale production make them ideal targets for genetic reprogramming. However, efforts in this area have been constrained by slow growth, long life cycles, the requirement for specialized facilities, a paucity of efficient tools for genetic manipulation, and the complexity of multicellularity. There is a need for better experimental and theoretical frameworks to understand the way genetic networks, cellular populations, and tissue-wide physical processes interact at different scales. We highlight new approaches to the DNA-based manipulation of plants and the use of advanced quantitative imaging techniques in simple plant models such as Marchantia polymorpha. These offer the prospects of improved understanding of plant dynamics and new approaches to rational engineering of plant traits.

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.