Modeling plant morphogenesis

Mathematical Modeling of Photo- and Thermomorphogenesis in Plants

Increased day lengths and warm conditions inversely affect plant growth by directly modulating nuclear phyB, ELF3, and COP1 levels. Quantitative measures of the hypocotyl length have been key to gaining a deeper understanding of this complex regulatory network, while similar quantitative data are the foundation for many studies in plant biology. Here, we explore the application of mathematical modeling, specifically ordinary differential equations (ODEs), to understand plant responses to these environmental cues. We provide a comprehensive guide to constructing, simulating, and fitting these models to data, using the law of mass action to study the evolution of molecular species. The fundamental principles of these models are introduced, highlighting their utility in deciphering complex plant physiological interactions and testing hypotheses. This brief introduction will not allow experimentalists without a mathematical background to run their own simulations overnight, but it will help them grasp modeling principles and communicate with more theory-inclined colleagues.

Combined computational modeling and experimental analysis integrating chemical and mechanical signals suggests possible mechanism of shoot meristem maintenance

Stem cell maintenance in multilayered shoot apical meristems (SAMs) of plants requires strict regulation of cell growth and division. Exactly how the complex milieu of chemical and mechanical signals interact in the central region of the SAM to regulate cell division plane orientation is not well understood. In this paper, simulations using a newly developed multiscale computational model are combined with experimental studies to suggest and test three hypothesized mechanisms for the regulation of cell division plane orientation and the direction of anisotropic cell expansion in the corpus. Simulations predict that in the Apical corpus, WUSCHEL and cytokinin regulate the direction of anisotropic cell expansion, and cells divide according to tensile stress on the cell wall. In the Basal corpus, model simulations suggest dual roles for WUSCHEL and cytokinin in regulating both the direction of anisotropic cell expansion and cell division plane orientation. Simulation results are followed by a detailed analysis of changes in cell characteristics upon manipulation of WUSCHEL and cytokinin in experiments that support model predictions. Moreover, simulations predict that this layer-specific mechanism maintains both the experimentally observed shape and structure of the SAM as well as the distribution of WUSCHEL in the tissue. This provides an additional link between the roles of WUSCHEL, cytokinin, and mechanical stress in regulating SAM growth and proper stem cell maintenance in the SAM.

Stability and convergence of the variable directions difference scheme for one nonlinear two-dimensional model

The system of two-dimensional nonlinear partial differential equations is considered. This system describes the vein formation in meristematic tissues of young leaves. Variable directions difference scheme is constructed and investigated. Absolute stability regarding space and time steps of scheme is shown. The convergence statement for the constructed scheme is proved. Rate of convergence is given. Various numerical experiments are carried out and results of some of them are considered in this paper. Comparison of numerical experiments with the results of the theoretical investigation is given too.

Can current crop models be used in the phenotyping era for predicting the genetic variability of yield of plants subjected to drought or high temperature?

A crop model with genetic inputs can potentially simulate yield for a large range of genotypes, sites, and years, thereby indicating where and when a given combination of alleles confers a positive effect. We discuss to what extent current crop models, developed for predicting the effects of climate or cultivation techniques on a reference genotype, are adequate for ranking yields of a large number of genotypes in climatic scenarios with water deficit or high temperatures. We compare here the algorithms involved in 19 crop models. Marked differences exist in the representation of the combined effects of temperature and water deficit on plant development, and in the coordination of these effects with biomass production. The current literature suggests that these differences have a small impact on the yield prediction of a reference genotype because errors on the effects of different traits compensate each other. We propose that they have a larger impact if the crop model is used in a genetic context, because the model has to account for the genetic variability of studied traits. Models with explicit genetic inputs will be increasingly feasible because model parameters corresponding to each genotype can now be measured in phenotyping platforms for large plant collections. This will in turn allow prediction of parameter values from the allelic composition of genotypes. It is therefore timely to adapt crop models to this new context to simulate the allelic effects in present or future climatic scenarios with water or heat stresses.

Advanced imaging techniques for the study of plant growth and development

A variety of imaging methodologies are being used to collect data for quantitative studies of plant growth and development from living plants. Multi-level data, from macroscopic to molecular, and from weeks to seconds, can be acquired. Furthermore, advances in parallelized and automated image acquisition enable the throughput to capture images from large populations of plants under specific growth conditions. Image-processing capabilities allow for 3D or 4D reconstruction of image data and automated quantification of biological features. These advances facilitate the integration of imaging data with genome-wide molecular data to enable systems-level modeling.

Computational models of plant development and form

The use of computational techniques increasingly permeates developmental biology, from the acquisition, processing and analysis of experimental data to the construction of models of organisms. Specifically, models help to untangle the non-intuitive relations between local morphogenetic processes and global patterns and forms. We survey the modeling techniques and selected models that are designed to elucidate plant development in mechanistic terms, with an emphasis on: the history of mathematical and computational approaches to developmental plant biology; the key objectives and methodological aspects of model construction; the diverse mathematical and computational methods related to plant modeling; and the essence of two classes of models, which approach plant morphogenesis from the geometric and molecular perspectives. In the geometric domain, we review models of cell division patterns, phyllotaxis, the form and vascular patterns of leaves, and branching patterns. In the molecular-level domain, we focus on the currently most extensively developed theme: the role of auxin in plant morphogenesis. The review is addressed to both biologists and computational modelers.

Modelling photo-modulated internode elongation in growing glasshouse cucumber canopies

• Growing glasshouse plant canopies are exposed to natural fluctuations in light quantity, and the dynamically changing canopy architecture induces local variations in light quality. This modelling study aimed to analyse the importance of both light signals for an accurate prediction of individual internode lengths. • We conceptualized two model approaches for estimating final internode lengths (FILs). The first one is only photosynthetically active radiation (PAR)-sensitive and ignores canopy architecture, whereas the second approach uses a functional-structural growth model for considering variations in both PAR and red : far-red (R : FR) ratio (L-Cucumber). Internode lengths measured in three experiments were used for model parameterization and evaluation. • The overall trends for the simulated FILs using the exclusively PAR-sensitive model approach were already in line with the measured FILs, but they underestimated FILs at higher ranks. L-Cucumber provided considerably better FIL predictions under various light conditions and canopy architectures. • Both light signals are needed for an accurate estimation of the FILs, and only L-Cucumber is able to consider R : FR signals from the growing canopy. Yet this study highlights the significance of the PAR signal for predicting FILs as neighbour effects increase, which indicates a potential role of photosynthate signalling in internode elongation.

Auxin transporters--why so many?

Interacting and coordinated auxin transporter actions in plants underlie a flexible network that mobilizes auxin in response to many developmental and environmental changes encountered by these sessile organisms. The independent but synergistic activity of individual transporters can be differentially regulated at various levels. This invests auxin transport mechanisms with robust functional redundancy and added auxin flow capacity when needed. An evolutionary perspective clarifies the roles of the different transporter groups in plant development. Mathematical and functional analysis of elements of auxin transport makes it possible to rationalize the relative contributions of members of the respective transporter classes to the localized auxin transport streams that then underlie both preprogrammed developmental changes and reactions to environmental stimuli.

The development of Arabidopsis as a model plant

Twenty-five years ago, Arabidopsis thaliana emerged as the model organism of choice for research in plant biology. A consensus was reached about the need to focus on a single organism to integrate the classical disciplines of plant science with the expanding fields of genetics and molecular biology. Ten years after publication of its genome sequence, Arabidopsis remains the standard reference plant for all of biology. We reflect here on the major advances and shared resources that led to the extraordinary growth of the Arabidopsis research community. We also underscore the importance of continuing to expand and refine our detailed knowledge of Arabidopsis while seeking to appreciate the remarkable diversity that characterizes the plant kingdom.

Computational morphodynamics: a modeling framework to understand plant growth

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

An auxin gradient and maximum in the Arabidopsis root apex shown by high-resolution cell-specific analysis of IAA distribution and synthesis

Local concentration gradients of the plant growth regulator auxin (indole-3-acetic acid [IAA]) are thought to instruct the positioning of organ primordia and stem cell niches and to direct cell division, expansion, and differentiation. High-resolution measurements of endogenous IAA concentrations in support of the gradient hypothesis are required to substantiate this hypothesis. Here, we introduce fluorescence-activated cell sorting of green fluorescent protein-marked cell types combined with highly sensitive mass spectrometry methods as a novel means for analyses of IAA distribution and metabolism at cellular resolution. Our results reveal the presence of IAA concentration gradients within the Arabidopsis thaliana root tip with a distinct maximum in the organizing quiescent center of the root apex. We also demonstrate that the root apex provides an important source of IAA and that cells of all types display a high synthesis capacity, suggesting a substantial contribution of local biosynthesis to auxin homeostasis in the root tip. Our results indicate that local biosynthesis and polar transport combine to produce auxin gradients and maxima in the root tip.

Plant intelligence: why, why not or where?

The concept of plant intelligence, as proposed by Anthony Trewavas, has raised considerable discussion. However, plant intelligence remains loosely defined; often it is either perceived as practically synonymous to Darwinian fitness, or reduced to a mere decorative metaphor. A more strict view can be taken, emphasizing necessary prerequisites such as memory and learning, which requires clarifying the definition of memory itself. To qualify as memories, traces of past events have to be not only stored, but also actively accessed. We propose a criterion for eliminating false candidates of possible plant intelligence phenomena in this stricter sense: an "intelligent" behavior must involve a component that can be approximated by a plausible algorithmic model involving recourse to stored information about past states of the individual or its environment. Re-evaluation of previously presented examples of plant intelligence shows that only some of them pass our test.

Leaf development: time to turn over a new leaf?

Molecular cloning of mutations affecting the morphology of plant leaves has proven to be useful for the causal analysis of leaf development. Studies of leaf mutants have produced a wealth of biologically meaningful information on the genes that participate in leaf initiation, leaf polarity specification and maintenance, and leaf expansion and maturation. The availability of collections of gene-indexed insertional mutants, automated platforms for high-throughput imaging, and new morphometry software is making genome-wide leaf phenomics possible and complements classical forward genetics approaches. Large-scale phenomic studies will further our understanding, among others, of two intriguing phenomena that recently reentered the leaf scenario. One is the unexpected relationship between translation and leaf dorsoventrality, recently confirmed by the severe abaxialization of double mutants involving loss-of-function alleles of the developmental selector genes AS1 and AS2 and some genes encoding ribosomal proteins. The second unexplained phenomenon is the compensatory cell enlargement experienced by some leaf mutants, in which a reduced cell number is compensated by their increased cell size compared with the wild type. This compensation suggests that cell cycling and cell enlargement are integrated in leaf primordia via cell-to-cell communication.

Different stresses, similar morphogenic responses: integrating a plethora of pathways

Exposure of plants to mild chronic stress can cause induction of specific, stress-induced morphogenic responses (SIMRs). These responses are characterized by a blockage of cell division in the main meristematic tissues, an inhibition of elongation and a redirected outgrowth of lateral organs. Key elements in the ontogenesis of this phenotype appear to be stress-affected gradients of reactive oxygen species (ROS), antioxidants, auxin and ethylene. These gradients are present at the the organismal level, but are integrated on the cellular level, affecting cell division, cell elongation and/or cell differentiation. Our analysis of the literature indicates that stress-induced modulation of plant growth is mediated by a plethora of molecular interactions, whereby different environmental signals can trigger similar morphogenic responses. At least some of the molecular interactions that underlie morphogenic responses appear to be interchangeable. We speculate that this complexity can be viewed in terms of a thermodynamic model, in which not the specific pathway, but the achieved metabolic state is biologically conserved.

NPY genes and AGC kinases define two key steps in auxin-mediated organogenesis in Arabidopsis

Auxin is an essential regulator of plant organogenesis. Most key genes in auxin biosynthesis, transport, and signaling belong to gene families, making it difficult to conduct genetic analysis of auxin action in plant development. Herein we report the functional analysis of several members of 2 gene families (NPY/ENP/MAB4 genes and AGC kinases) in auxin-mediated organogenesis and their relationships with the YUC family of flavin monooxygenases that are essential for auxin biosynthesis. We show that 5 NPY genes (NPY1 to NPY5) and 4 AGC kinases (PID, PID2, WAG1, and WAG2) have distinct, yet overlapping, expression patterns. Disruption of NPY1 does not cause obvious defects in organogenesis, but npy1 npy3 npy5 triple mutants failed to make flower primordia, a phenotype that is also observed when AGC kinase PID is compromised. Inactivation of YUC1 and YUC4 in npy1 background also phenocopies npy1 npy3 npy5 and pid. Simultaneous disruption of PID and its 3 closest homologs (PID2, WAG1, and WAG2) completely abolishes the formation of cotyledons, which phenocopies npy1 pid double mutants and yuc1 yuc4 pid triple mutants. Our results demonstrate that NPY genes and AGC kinases define 2 key steps in a pathway that controls YUC-mediated organogenesis in Arabidopsis.

A stochastic 1D nearest-neighbour automaton models early development of the brown alga Ectocarpus siliculosus

Early development of the filamentous brown alga Ectocarpus siliculosus (Dillwyn) Lyngbye involves two cell types that are arranged in a polymorphic, but constrained, pattern. The present study aimed to decipher the cellular processes responsible for the establishment of this pattern. Thorough observations characterised five different events of division and differentiation that occurred during the early development. The hypothesis that a local control is responsible for these processes was tested. To do so, Ectomat, a stochastic automaton in which each cell only interacts with its closest neighbour(s), was created. The probabilities for the five events were adjusted to fit to the observations. Simulations with Ectomat reconstructed most of the essential properties of the sporophyte development, in terms of cell-type proportion, relative position and growth dynamics. The whole organism properties emerged by applying local transition rules. In conclusion, no global position information system was required at this development stage. Randomly occurring cell events, driven by simple contact interactions, are sufficient to account for the early filament development and establishment of the cell-type pattern of E. siliculosus.

Transcription factors relevant to auxin signalling coordinate broad-spectrum metabolic shifts including sulphur metabolism

A systems approach has previously been used to follow the response behaviour of Arabidopsis thaliana plants upon sulphur limitation. A response network was reconstructed from a time series of transcript and metabolite profiles, integrating complex metabolic and transcript data in order to investigate a potential causal relationship. The resulting scale-free network allowed potential transcriptional regulators of sulphur metabolism to be identified. Here, three sulphur-starvation responsive transcription factors, IAA13, IAA28, and ARF-2 (ARF1-Binding Protein), all of which are related to auxin signalling, were selected for further investigation. IAA28 overexpressing and knock-down lines showed no major morphological changes, whereas IAA13- and ARF1-BP-overexpressing plants grew more slowly than the wild type. Steady-state metabolite levels and expression of pathway-relevant genes were monitored under normal and sulphate-depleted conditions. For all lines, changes in transcript and metabolite levels were observed, yet none of these changes could exclusively be linked to sulphur stress. Instead, up- or down-regulation of the transcription factors caused metabolic changes which in turn affected sulphur metabolism. Auxin-relevant transcription factors are thus part of a complex response pattern to nutrient starvation that serve as coordinators of the metabolic shifts driving sulphur homeostasis rather then as direct effectors of the sulphate assimilation pathway. This study provides the first evidence ever presented that correlates auxin-related transcriptional regulators with primary plant metabolism.

Computer models of auxin transport: a review and commentary

With the recent proliferation of computer models of auxin transport, it is important that plant biologists understand something about these techniques and how to evaluate them. The paper begins with a brief introduction to the parts of a computer model, followed by a discussion of the limitations of the most common auxin modelling technique. Lastly, several recent models of organ initiation in the shoot apical meristem (i.e. phyllotaxis) are reviewed. The cell and molecular biology of phyllotaxis is now understood well enough that computer models can go beyond a simple 'proof of principle' and start to provide insights into gene function.

Patterns of beauty--omics meets plant development

Developmental biology aims to identify mechanisms that govern cell proliferation and differentiation in the body plan formation of multicellular organisms. In the past, developmental biologists described how anatomy and morphology are established during ontogenesis, and developmental geneticists identified many developmental regulators. In contrast to the traditional approaches that mostly focus on one or a few genes at a time, highly parallel profiling technologies have been developed for use in biological research over the past decade. Such parallel profiling technologies probe many genes, transcripts, proteins or metabolites at once. In this review, I discuss the growing impact of transcriptomics, proteomics, metabolomics and modelling on plant developmental biology. Novel profiling technologies will not make traditional gene-centred approaches obsolete but should instead complement forward developmental genetics.