A dynamic model for stem cell homeostasis and patterning in Arabidopsis meristems

An updated model of shoot apical meristem regulation by ERECTA family and CLAVATA3 signaling pathways in Arabidopsis

The shoot apical meristem (SAM) gives rise to the aboveground organs of plants. The size of the SAM is relatively constant due to the balance between stem cell replenishment and cell recruitment into new organs. In angiosperms, the transcription factor WUSCHEL (WUS) promotes stem cell proliferation in the central zone of the SAM. WUS forms a negative feedback loop with a signaling pathway activated by CLAVATA3 (CLV3). In the periphery of the SAM, the ERECTA family receptors (ERfs) constrain WUS and CLV3 expression. Here, we show that four ligands of ERfs redundantly inhibit the expression of these two genes. Transcriptome analysis confirmed that WUS and CLV3 are the main targets of ERf signaling and uncovered new ones. Analysis of promoter reporters indicated that the WUS expression domain mostly overlaps with the CLV3 domain and does not shift along the apical-basal axis in clv3 mutants. Our three-dimensional mathematical model captured gene expression distributions at the single-cell level under various perturbed conditions. Based on our findings, CLV3 regulates cellular levels of WUS mostly through autocrine signaling, and ERfs regulate the spatial expression of WUS, preventing its encroachment into the peripheral zone.

Developmental timing in plants

Plants exhibit reproducible timing of developmental events at multiple scales, from switches in cell identity to maturation of the whole plant. Control of developmental timing likely evolved for similar reasons that humans invented clocks: to coordinate events. However, whereas clocks are designed to run independently of conditions, plant developmental timing is strongly dependent on growth and environment. Using simplified models to convey key concepts, we review how growth-dependent and inherent timing mechanisms interact with the environment to control cyclical and progressive developmental transitions in plants.

Molecular Mechanisms of Regulation of Root Development by Plant Peptides

Peptides perform many functions, participating in the regulation of cell differentiation, regulating plant growth and development, and also involved in the response to stress factors and in antimicrobial defense. Peptides are an important class biomolecules for intercellular communication and in the transmission of various signals. The intercellular communication system based on the ligand-receptor bond is one of the most important molecular bases for creating complex multicellular organisms. Peptide-mediated intercellular communication plays a critical role in the coordination and determination of cellular functions in plants. The intercellular communication system based on the receptor-ligand is one of the most important molecular foundations for creating complex multicellular organisms. Peptide-mediated intercellular communication plays a critical role in the coordination and determination of cellular functions in plants. The identification of peptide hormones, their interaction with receptors, and the molecular mechanisms of peptide functioning are important for understanding the mechanisms of both intercellular communications and for regulating plant development. In this review, we drew attention to some peptides involved in the regulation of root development, which implement this regulation by the mechanism of a negative feedback loop.

Nucleation of stem cell domains in a bistable activator-inhibitor model of the shoot apical meristem

Shoot apical meristems (SAMs) give rise to all above-ground tissues of a plant. Expansion of meristematic tissue is derived from the growth and division of stem cells that reside in a central zone of the SAM. This reservoir of stem cells is maintained by expression of a transcription factor WUSCHEL that is responsible for the development of stem cells in the central zone. WUSCHEL expression is self-activating and downregulated by a signaling pathway initiated by CLAVATA proteins, which are upregulated by WUSCHEL. This classic activator-inhibitor network can generate localized patterns of WUSCHEL activity by a Turing instability provided certain constraints on reaction rates and diffusion constants of WUSCHEL and CLAVATA are satisfied, and most existing mathematical models of nucleation and confinement of stem cells in the SAM rely on Turing's mechanism. However, Turing patterns have certain properties that are inconsistent with observed patterns of stem cell differentiation in the SAM. As an alternative mechanism, we propose a model for stem cell confinement based on a bistable-switch in WUSCHEL-CLAVATA interactions. We study the bistable-switch mechanism for pattern formation in a spatially continuous domain and in a discrete cellularized tissue in the presence of a non-uniform field of a rapidly diffusing hormone. By comparing domain formation by Turing and bistable-switch mechanisms in these contexts, we show that bistable switching provides a superior account of nucleation and confinement of the stem cell domain under reasonable assumptions on reaction rates and diffusion constants.

Control of Arabidopsis shoot stem cell homeostasis by two antagonistic CLE peptide signalling pathways

Stem cell homeostasis in plant shoot meristems requires tight coordination between stem cell proliferation and cell differentiation. In Arabidopsis, stem cells express the secreted dodecapeptide CLAVATA3 (CLV3), which signals through the leucine-rich repeat (LRR)-receptor kinase CLAVATA1 (CLV1) and related CLV1-family members to downregulate expression of the homeodomain transcription factor WUSCHEL (WUS). WUS protein moves from cells below the stem cell domain to the meristem tip and promotes stem cell identity, together with CLV3 expression, generating a negative feedback loop. How stem cell activity in the meristem centre is coordinated with organ initiation and cell differentiation at the periphery is unknown. We show here that the CLE40 gene, encoding a secreted peptide closely related to CLV3, is expressed in the SAM in differentiating cells in a pattern complementary to that of CLV3. CLE40 promotes WUS expression via BAM1, a CLV1-family receptor, and CLE40 expression is in turn repressed in a WUS-dependent manner. Together, CLE40-BAM1-WUS establish a second negative feedback loop. We propose that stem cell homeostasis is achieved through two intertwined pathways that adjust WUS activity and incorporate information on the size of the stem cell domain, via CLV3-CLV1, and on cell differentiation via CLE40-BAM1.

What shoots can teach about theories of plant form

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

A mathematical model for understanding synergistic regulations and paradoxical feedbacks in the shoot apical meristem

The shoot apical meristem (SAM) is the primary stem cell niche in plant shoots. Stem cells in the SAM are controlled by an intricate regulatory network, including negative feedback between WUSCHEL (WUS) and CLAVATA3 (CLV3). Recently, we identified a group of signals, Epidermal Patterning Factor-Like (EPFL) proteins, that are produced at the peripheral region and are important for SAM homeostasis. Here, we present a mathematical model for the SAM regulatory network. The model revealed that the SAM uses EPFL and signals such as HAIRY MERISTEM from the middle in a synergistic manner to constrain both WUS and CLV3. We found that interconnected negative and positive feedbacks between WUS and CLV3 ensure stable WUS expression in the SAM when facing perturbations, and the positive feedback loop also maintains distinct cell populations containing WUS on and CLV3 on cells in the apical-basal direction. Furthermore, systematic perturbations of the parameters revealed a tradeoff between optimizations of multiple patterning features. Our results provide a holistic view of the regulation of SAM patterning in multiple dimensions. They give insights into how Arabidopsis integrates signals from lateral and apical-basal axes to control the SAM patterning, and they shed light into design principles that may be widely useful for understanding regulatory networks of stem cell niche.

AMP1 and CYP78A5/7 act through a common pathway to govern cell fate maintenance in Arabidopsis thaliana

Higher plants can continuously form new organs by the sustained activity of pluripotent stem cells. These stem cells are embedded in meristems, where they produce descendants, which undergo cell proliferation and differentiation programs in a spatiotemporally-controlled manner. Under certain conditions, pluripotency can be reestablished in descending cells and this reversion in cell fate appears to be actively suppressed by the existing stem cell pool. Mutation of the putative carboxypeptidase ALTERED MERISTEM PROGRAM1 (AMP1) in Arabidopsis causes defects in the suppression of pluripotency in cells normally programmed for differentiation, giving rise to unique hypertrophic phenotypes during embryogenesis as well as in the shoot apical meristem. A role of AMP1 in the miRNA-dependent control of translation has recently been established, however, how this activity is connected to its developmental functions is not resolved. Here we identify members of the cytochrome P450 clade CYP78A to act in parallel with AMP1 to control cell fate in Arabidopsis. Mutation of CYP78A5 and its close homolog CYP78A7 in a cyp78a5,7 double mutant caused suspensor-to-embryo conversion and ectopic stem cell pool formation in the shoot meristem, phenotypes characteristic for amp1. The tissues affected in the mutants showed pronounced expression levels of AMP1 and CYP78A5 in wild type. A comparison of mutant transcriptomic responses revealed an intriguing degree of overlap and highlighted alterations in protein lipidation processes. Moreover, we also found elevated protein levels of selected miRNA targets in cyp78a5,7. Based on comprehensive genetic interaction studies we propose a model in which both enzyme classes act on a common downstream process to sustain cell fate decisions in the early embryo and the shoot apical meristem.

The interaction of transcription factors controls the spatial layout of plant aerial stem cell niches

The plant shoot apical meristem holds a stem cell niche from which all aerial organs originate. Using a computational approach we show that a mixture of monomers and heterodimers of the transcription factors WUSCHEL and HAIRY MERISTEM is sufficient to pattern the stem cell niche, and predict that immobile heterodimers form a regulatory "pocket" surrounding the stem cells. The model achieves to reproduce an array of perturbations, including mutants and tissue size modifications. We also show its ability to reproduce the recently observed dynamical shift of the stem cell niche during the development of an axillary meristem. The work integrates recent experimental results to answer the longstanding question of how the asymmetry of expression between the stem cell marker CLAVATA3 and its activator WUSCHEL is achieved, and recent findings of plasticity in the system.

Descriptive Modeling of the Dynamical Systems and Determination of Feedback Homeostasis at Different Levels of Life Organization

The state-of-art research in the field of life's organization confronts the need to investigate a number of interacting components, their properties and conditions of sustainable behaviour within a natural system. In biology, ecology and life sciences, the performance of such stable system is usually related to homeostasis, a property of the system to actively regulate its state within a certain allowable limits. In our previous work, we proposed a deterministic model for systems' homeostasis. The model was based on dynamical system's theory and pairwise relationships of competition, amensalism and antagonism taken from theoretical biology and ecology. However, the present paper proposes a different dimension to our previous results based on the same model. In this paper, we introduce the influence of inter-component relationships in a system, wherein the impact is characterized by direction (neutral, positive, or negative) as well as its (absolute) value, or strength. This makes the model stochastic which, in our opinion, is more consistent with real-world elements affected by various random factors. The case study includes two examples from areas of hydrobiology and medicine. The models acquired for these cases enabled us to propose a convincing explanation for corresponding phenomena identified by different types of natural systems.

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

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

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

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

Centering the Organizing Center in the Arabidopsis thaliana Shoot Apical Meristem by a Combination of Cytokinin Signaling and Self-Organization

Plants have the ability to continously generate new organs by maintaining populations of stem cells throught their lives. The shoot apical meristem (SAM) provides a stable environment for the maintenance of stem cells. All cells inside the SAM divide, yet boundaries and patterns are maintained. Experimental evidence indicates that patterning is independent of cell lineage, thus a dynamic self-regulatory mechanism is required. A pivotal role in the organization of the SAM is played by the WUSCHEL gene (WUS). An important question in this regard is that how WUS expression is positioned in the SAM via a cell-lineage independent signaling mechanism. In this study we demonstrate via mathematical modeling that a combination of an inhibitor of the Cytokinin (CK) receptor, Arabidopsis histidine kinase 4 (AHK4) and two morphogens originating from the top cell layer, can plausibly account for the cell lineage-independent centering of WUS expression within SAM. Furthermore, our laser ablation and microsurgical experiments support the hypothesis that patterning in SAM occurs at the level of CK reception and signaling. The model suggests that the interplay between CK signaling, WUS/CLV feedback loop and boundary signals can account for positioning of the WUS expression, and provides directions for further experimental investigation.

ALTERED MERISTEM PROGRAM1 suppresses ectopic stem cell niche formation in the shoot apical meristem in a largely cytokinin-independent manner

Plants are able to reiteratively form new organs in an environmentally adaptive manner during postembryonic development. Organ formation in plants is dependent on stem cell niches (SCNs), which are located in the so-called meristems. Meristems show a functional zonation along the apical-basal axis and the radial axis. Shoot apical meristems of higher plants are dome-like structures, which contain a central SCN that consists of an apical stem cell pool and an underlying organizing center. Organ primordia are formed in the circular peripheral zone (PZ) from stem cell descendants in which differentiation programs are activated. One mechanism to keep this radial symmetry integrated is that the existing SCN actively suppresses stem cell identity in the PZ. However, how this lateral inhibition system works at the molecular level is far from understood. Here, we show that a defect in the putative carboxypeptidase ALTERED MERISTEM PROGRAM1 (AMP1) causes the formation of extra SCNs in the presence of an intact primary shoot apical meristem, which at least partially contributes to the enhanced shoot meristem size and leaf initiation rate found in the mutant. This defect appears to be neither a specific consequence of the altered cytokinin levels in amp1 nor directly mediated by the WUSCHEL/CLAVATA feedback loop. De novo formation of supernumerary stem cell pools was further enhanced in plants mutated in both AMP1 and its paralog LIKE AMP1, indicating that they exhibit partially overlapping roles to suppress SCN respecification in the PZ.

Domain nucleation and confinement in agent-controlled bistable systems

We report a mechanism of pattern formation in growing bistable systems coupled indirectly. A modified Fujita et al. model is studied as an example of a reaction-diffusion system of nondiffusive activator and inhibitor molecules immersed in the medium of a fast diffusive agent. Here we show that, as the system grows, a new domain nucleates spontaneously in the area where the local level of the agent becomes critical. Newly nucleated domains are stable and the pattern formation is different from Turing's mechanism in monostable systems. Domains are spatially confined by the agent even if the activator and inhibitor molecules diffuse. With the spatial extension of the system, a larger domain may undergo a wave number instability, and the concentrations of active molecules within the neighboring elements of a domain can become sharply different. The mechanism reported in this work could be generic for pattern formation systems involving multistability, growth, and indirect coupling.

Modelling hormonal response and development

As our knowledge of the complexity of hormone homeostasis, transport, perception, and response increases, and their outputs become less intuitive, modelling is set to become more important. Initial modelling efforts have focused on hormone transport and response pathways. However, we now need to move beyond the network scales and use multicellular and multiscale modelling approaches to predict emergent properties at different scales. Here we review some examples where such approaches have been successful, for example, auxin-cytokinin crosstalk regulating root vascular development or a study of lateral root emergence where an iterative cycle of modelling and experiments lead to the identification of an overlooked role for PIN3. Finally, we discuss some of the remaining biological and technical challenges.

Leaf development: a cellular perspective

Through its photosynthetic capacity the leaf provides the basis for growth of the whole plant. In order to improve crops for higher productivity and resistance for future climate scenarios, it is important to obtain a mechanistic understanding of leaf growth and development and the effect of genetic and environmental factors on the process. Cells are both the basic building blocks of the leaf and the regulatory units that integrate genetic and environmental information into the developmental program. Therefore, to fundamentally understand leaf development, one needs to be able to reconstruct the developmental pathway of individual cells (and their progeny) from the stem cell niche to their final position in the mature leaf. To build the basis for such understanding, we review current knowledge on the spatial and temporal regulation mechanisms operating on cells, contributing to the formation of a leaf. We focus on the molecular networks that control exit from stem cell fate, leaf initiation, polarity, cytoplasmic growth, cell division, endoreduplication, transition between division and expansion, expansion and differentiation and their regulation by intercellular signaling molecules, including plant hormones, sugars, peptides, proteins, and microRNAs. We discuss to what extent the knowledge available in the literature is suitable to be applied in systems biology approaches to model the process of leaf growth, in order to better understand and predict leaf growth starting with the model species Arabidopsis thaliana.

A basic set of homeostatic controller motifs

Adaptation and homeostasis are essential properties of all living systems. However, our knowledge about the reaction kinetic mechanisms leading to robust homeostatic behavior in the presence of environmental perturbations is still poor. Here, we describe, and provide physiological examples of, a set of two-component controller motifs that show robust homeostasis. This basic set of controller motifs, which can be considered as complete, divides into two operational work modes, termed as inflow and outflow control. We show how controller combinations within a cell can integrate uptake and metabolization of a homeostatic controlled species and how pathways can be activated and lead to the formation of alternative products, as observed, for example, in the change of fermentation products by microorganisms when the supply of the carbon source is altered. The antagonistic character of hormonal control systems can be understood by a combination of inflow and outflow controllers.

Modeling regulatory networks to understand plant development: small is beautiful

We now have unprecedented capability to generate large data sets on the myriad genes and molecular players that regulate plant development. Networks of interactions between systems components can be derived from that data in various ways and can be used to develop mathematical models of various degrees of sophistication. Here, we discuss why, in many cases, it is productive to focus on small networks. We provide a brief and accessible introduction to relevant mathematical and computational approaches to model regulatory networks and discuss examples of small network models that have helped generate new insights into plant biology (where small is beautiful), such as in circadian rhythms, hormone signaling, and tissue patterning. We conclude by outlining some of the key technical and modeling challenges for the future.

Peptides and receptors controlling root development

The growth of a plant's root system depends on the continued activity of the root meristem, and the generation of new meristems when lateral roots are initiated. Plants have developed intricate signalling systems that employ secreted peptides and plasma membrane-localized receptor kinases for short- and long-range communication. Studies on growth of the vascular system, the generation of lateral roots, the control of cell differentiation in the root meristem and the interaction with invading pathogens or symbionts has unravelled a network of peptides and receptor systems with occasionally shared functions. A common theme is the employment of conserved modules, consisting of a short signalling peptide, a receptor-like kinase and a target transcription factor, that control the fate and proliferation of stem cells during root development. This review intends to give an overview of the recent advances in receptor and peptide ligand-mediated signalling involved in root development.

Cytokinin signaling as a positional cue for patterning the apical-basal axis of the growing Arabidopsis shoot meristem

The transcription factor WUSCHEL (WUS) acts from a well-defined domain within the Arabidopsis thaliana shoot apical meristem (SAM) to maintain a stem cell niche. A negative-feedback loop involving the CLAVATA (CLV) signaling pathway regulates the number of WUS-expressing cells and provides the current paradigm for the homeostatic maintenance of stem cell numbers. Despite the continual turnover of cells in the SAM during development, the WUS domain remains patterned at a fixed distance below the shoot apex. Recent work has uncovered a positive-feedback loop between WUS function and the plant hormone cytokinin. Furthermore, loss of function of the cytokinin biosynthetic gene, LONELY GUY (LOG), results in a wus-like phenotype in rice. Herein, we find the Arabidopsis LOG4 gene is expressed in the SAM epidermis. We use this to develop a computational model representing a growing SAM to suggest the plausibility that apically derived cytokinin and CLV signaling, together, act as positional cues for patterning the WUS domain within the stem cell niche. Furthermore, model simulations backed by experimental data suggest a previously unknown negative feedback between WUS function and cytokinin biosynthesis in the Arabidopsis SAM epidermis. These results suggest a plausible dynamic feedback principle by which the SAM stem cell niche is patterned.

On evaluating models in Computational Morphodynamics

Recent advances in experimental plant biology have led to an increased potential to investigate plant development at a systems level. The emerging research field of Computational Morphodynamics has the aim to lead this development by combining dynamic spatial experimental data with computational models of molecular networks, growth, and mechanics in a multicellular context. The increased number of published models may lead to a diversification of our understanding of the systems, and methods for evaluating, comparing, and sharing models are main challenges for the future. We will discuss this problem using ideas originating from physics and use recent computational models of plant development as examples.

WUSCHEL protein movement mediates stem cell homeostasis in the Arabidopsis shoot apex

WUSCHEL (WUS) is a homeodomain transcription factor produced in cells of the niche/organizing center (OC) of shoot apical meristems. WUS specifies stem cell fate and also restricts its own levels by activating a negative regulator, CLAVATA3 (CLV3), in adjacent cells of the central zone (CZ). Here we show that the WUS protein, after being synthesized in cells of the OC, migrates into the CZ, where it activates CLV3 transcription by binding to its promoter elements. Using a computational model, we show that maintenance of the WUS gradient is essential to regulate stem cell number. Migration of a stem cell-inducing transcription factor into adjacent cells to activate a negative regulator, thereby restricting its own accumulation, is a theme that is unique to plant stem cell niches.

The Function of the CLE Peptides in Plant Development and Plant-Microbe Interactions

The CLAVATA3 (CLV3)/ENDOSPERM SURROUNDING REGION (ESR) (CLE) peptides consist of 12 or 13 amino acids, including hydroxylated proline residues that may or may not contain sugar modifications, and function in a non-cell-autonomous fashion. The CLE gene was first reported in Zea mays (maize) as an endosperm-specific gene, ESR, in 1997 (Opsahl-Ferstad et al., 1997). CLE genes encode secreted peptides that function in the extracellular space as intercellular signaling molecules and bind to cellular surface receptor-like proteins to transmit a signal. CLE peptides regulate various physiological and developmental processes and its signaling pathway are conserved in diverse land plants. Recent CLE functional studies have pointed to their significance in regulating meristematic activity in plant meristems, through the CLE-receptor kinase-WOX signaling node. CLV3 and CLE40 are responsible for maintenance of shoot apical meristem (SAM) and root apical meristem (RAM) function, regulating homeodomain transcription factors, WUSCHEL (WUS) and WUSCHEL-related homeobox 5 (WOX5), respectively. CLE and WOX form an interconnected and self-correcting feedback loop to provide robustness to stem cell homeostasis. CLE peptides are required for certain plant-microbe interactions, such as those that occur during legume symbiosis and phytopathogenic nematode infection. Understanding the molecular properties of CLE peptides may provide insight into plant cell-cell communication, and therefore also into plant-microbe interactions.

Organogenesis from stem cells in planta: multiple feedback loops integrating molecular and mechanical signals

In multicellular organisms, the coordination of cell behaviors largely relies on biochemical and biophysical signals. Understanding how such signals control development is often challenging, because their distribution relies on the activity of individual cells and, in a feedback loop, on tissue behavior and geometry. This review focuses on one of the best-studied structures in biology, the shoot apical meristem (SAM). This tissue is responsible for the production of all the aerial parts of a plant. In the SAM, a population of stem cells continuously produces new cells that are incorporated in lateral organs, such as leaves, branches, and flowers. Organogenesis from stem cells involves a tight regulation of cell identity and patterning as well as large-scale morphogenetic events. The gene regulatory network controlling these processes is highly coordinated in space by various signals, such as plant hormones, peptides, intracellular mobile factors, and mechanical stresses. Many crosstalks and feedback loops interconnecting these pathways have emerged in the past 10 years. The plant hormone auxin and mechanical forces have received more attention recently and their role is more particularly detailed here. An integrated view of these signaling networks is also presented in order to help understanding how robust shape and patterning can emerge from these networks.

Computational morphodynamics of plants: integrating development over space and time

The emerging field of computational morphodynamics aims to understand the changes that occur in space and time during development by combining three technical strategies: live imaging to observe development as it happens; image processing and analysis to extract quantitative information; and computational modelling to express and test time-dependent hypotheses. The strength of the field comes from the iterative and combined use of these techniques, which has provided important insights into plant development.

Reaction-diffusion pattern in shoot apical meristem of plants

A fundamental question in developmental biology is how spatial patterns are self-organized from homogeneous structures. In 1952, Turing proposed the reaction-diffusion model in order to explain this issue. Experimental evidence of reaction-diffusion patterns in living organisms was first provided by the pigmentation pattern on the skin of fishes in 1995. However, whether or not this mechanism plays an essential role in developmental events of living organisms remains elusive. Here we show that a reaction-diffusion model can successfully explain the shoot apical meristem (SAM) development of plants. SAM of plants resides in the top of each shoot and consists of a central zone (CZ) and a surrounding peripheral zone (PZ). SAM contains stem cells and continuously produces new organs throughout the lifespan. Molecular genetic studies using Arabidopsis thaliana revealed that the formation and maintenance of the SAM are essentially regulated by the feedback interaction between WUSHCEL (WUS) and CLAVATA (CLV). We developed a mathematical model of the SAM based on a reaction-diffusion dynamics of the WUS-CLV interaction, incorporating cell division and the spatial restriction of the dynamics. Our model explains the various SAM patterns observed in plants, for example, homeostatic control of SAM size in the wild type, enlarged or fasciated SAM in clv mutants, and initiation of ectopic secondary meristems from an initial flattened SAM in wus mutant. In addition, the model is supported by comparing its prediction with the expression pattern of WUS in the wus mutant. Furthermore, the model can account for many experimental results including reorganization processes caused by the CZ ablation and by incision through the meristem center. We thus conclude that the reaction-diffusion dynamics is probably indispensable for the SAM development of plants.

Reaction-diffusion pattern in shoot apical meristem of plants

A fundamental question in developmental biology is how spatial patterns are self-organized from homogeneous structures. In 1952, Turing proposed the reaction-diffusion model in order to explain this issue. Experimental evidence of reaction-diffusion patterns in living organisms was first provided by the pigmentation pattern on the skin of fishes in 1995. However, whether or not this mechanism plays an essential role in developmental events of living organisms remains elusive. Here we show that a reaction-diffusion model can successfully explain the shoot apical meristem (SAM) development of plants. SAM of plants resides in the top of each shoot and consists of a central zone (CZ) and a surrounding peripheral zone (PZ). SAM contains stem cells and continuously produces new organs throughout the lifespan. Molecular genetic studies using Arabidopsis thaliana revealed that the formation and maintenance of the SAM are essentially regulated by the feedback interaction between WUSHCEL (WUS) and CLAVATA (CLV). We developed a mathematical model of the SAM based on a reaction-diffusion dynamics of the WUS-CLV interaction, incorporating cell division and the spatial restriction of the dynamics. Our model explains the various SAM patterns observed in plants, for example, homeostatic control of SAM size in the wild type, enlarged or fasciated SAM in clv mutants, and initiation of ectopic secondary meristems from an initial flattened SAM in wus mutant. In addition, the model is supported by comparing its prediction with the expression pattern of WUS in the wus mutant. Furthermore, the model can account for many experimental results including reorganization processes caused by the CZ ablation and by incision through the meristem center. We thus conclude that the reaction-diffusion dynamics is probably indispensable for the SAM development of plants.

Models of sequestration and receptor cross-talk for explaining multiple mutants in plant stem cell regulation

BACKGROUND

Stem cells reside in a plant's shoot meristem throughout its life and are main regulators of above-ground plant development. The stem cell maintenance depends on a feedback network between the CLAVATA and WUSCHEL genes. The CLAVATA3 peptide binds to the CLAVATA1 receptor leading to WUSCHEL inhibition. WUSCHEL, on the other hand, activates CLAVATA3 expression. Recent experiments suggest a second pathway where CLAVATA3 inhibits WUSCHEL via the CORYNE receptor pathway. An interesting question, central for understanding the receptor signaling, is why the clavata1-11 null mutant has a weaker phenotype compared with the clavata1-1 non-null mutant. It has been suggested that this relies on interference from the mutated CLAVATA1 acting on the CORYNE pathway.

RESULTS

We present two models for the CLAVATA-WUSCHEL feedback network including two receptor pathways for WUSCHEL repression and differing only by the hypothesized mechanisms for the clavata1-1 non-null mutant. The first model is an implementation of the previously suggested interference mechanism. The other model assumes an unaltered binding between CLAVATA3 and the mutated CLAVATA1 but with a loss of propagated signal into the cell. We optimize the models using data from wild type and four single receptor mutant experiments and use data from two receptor double mutant experiments in a validation step. Both models are able to explain all seven phenotypes and in addition qualitatively predict CLAVATA3 perturbations. The two models for the clavata1-1 mutant differ in the direct mechanism of the mutant, but they also predict other differences in the dynamics of the stem cell regulating network. We show that the interference hypothesis leads to an abundance of receptors, while the loss-of-signal hypothesis leads to sequestration of CLAVATA3 and relies on degradation or internalization of the bound CLAVATA1 receptor.

CONCLUSIONS

Using computational modeling, we show that an interference hypothesis and a more parsimonious loss-of-signal hypothesis for a clavata1 non-null mutant both lead to behaviors predicting wild type and six receptor mutant experiments. Although the two models have identical implementations of the unperturbed feedback network for stem cell regulation, we can point out model-predicted differences that may be resolved in future experiments.

Epidermis: the formation and functions of a fundamental plant tissue

Epidermis differentiation and maintenance are essential for plant survival. Constant cross-talk between epidermal cells and their immediate environment is at the heart of epidermal cell fate, and regulates epidermis-specific transcription factors. These factors in turn direct epidermal differentiation involving a whole array of epidermis-specific pathways including specialized lipid metabolism necessary to build the protective cuticle layer. An intact epidermis is crucial for certain key processes in plant development, shoot growth and plant defence. Here, we discuss the control of epidermal cell fate and the function of the epidermal cell layer in the light of recent advances in the field.

The vascular cambium: molecular control of cellular structure

Indeterminate growth and the production of new organs in plants require a constant supply of new cells. The majority of these cells are produced in mitotic regions called meristems. For primary or tip growth of the roots and shoots, the meristems are located in the apices. These apical meristems have been shown to function as developmentally regulated and environmentally responsive stem cell niches. The principle requirements to maintain a functioning meristem in a dynamic system are a balance of cell division and differentiation and the regulation of the planes of cell division and expansion. Woody plants also have secondary indeterminate mitotic regions towards the exterior of roots, stems and branches that produce the cells for continued growth in girth. The chief secondary meristem is the vascular cambium (VC). As its name implies, cells produced in the VC contribute to the growth in girth via the production of secondary vascular elements. Although we know a considerable amount about the cellular and molecular basis of the apical meristems, our knowledge of the cellular basis and molecular functioning of the VC has been rudimentary. This is now changing as a growing body of research shows that the primary and secondary meristems share some common fundamental regulatory mechanisms. In this review, we outline recent research that is leading to a better understanding of the molecular forces that shape the cellular structure and function of the VC.

Single-cell and coupled GRN models of cell patterning in the Arabidopsis thaliana root stem cell niche

BACKGROUND

Recent experimental work has uncovered some of the genetic components required to maintain the Arabidopsis thaliana root stem cell niche (SCN) and its structure. Two main pathways are involved. One pathway depends on the genes SHORTROOT and SCARECROW and the other depends on the PLETHORA genes, which have been proposed to constitute the auxin readouts. Recent evidence suggests that a regulatory circuit, composed of WOX5 and CLE40, also contributes to the SCN maintenance. Yet, we still do not understand how the niche is dynamically maintained and patterned or if the uncovered molecular components are sufficient to recover the observed gene expression configurations that characterize the cell types within the root SCN. Mathematical and computational tools have proven useful in understanding the dynamics of cell differentiation. Hence, to further explore root SCN patterning, we integrated available experimental data into dynamic Gene Regulatory Network (GRN) models and addressed if these are sufficient to attain observed gene expression configurations in the root SCN in a robust and autonomous manner.

RESULTS

We found that an SCN GRN model based only on experimental data did not reproduce the configurations observed within the root SCN. We developed several alternative GRN models that recover these expected stable gene configurations. Such models incorporate a few additional components and interactions in addition to those that have been uncovered. The recovered configurations are stable to perturbations, and the models are able to recover the observed gene expression profiles of almost all the mutants described so far. However, the robustness of the postulated GRNs is not as high as that of other previously studied networks.

CONCLUSIONS

These models are the first published approximations for a dynamic mechanism of the A. thaliana root SCN cellular pattering. Our model is useful to formally show that the data now available are not sufficient to fully reproduce root SCN organization and genetic profiles. We then highlight some experimental holes that remain to be studied and postulate some novel gene interactions. Finally, we suggest the existence of a generic dynamical motif that can be involved in both plant and animal SCN maintenance.

A hierarchical approach to model parameter optimization for developmental systems

In the context of Systems Biology, computer simulations of gene regulatory networks provide a powerful tool to validate hypotheses and to explore possible system behaviors. Nevertheless, modeling a system poses some challenges of its own: especially the step of model calibration is often difficult due to insufficient data. For example when considering developmental systems, mostly qualitative data describing the developmental trajectory is available while common calibration techniques rely on high-resolution quantitative data. Focusing on the calibration of differential equation models for developmental systems, this study investigates different approaches to utilize the available data to overcome these difficulties. More specifically, the fact that developmental processes are hierarchically organized is exploited to increase convergence rates of the calibration process as well as to save computation time. Using a gene regulatory network model for stem cell homeostasis in Arabidopsis thaliana the performance of the different investigated approaches is evaluated, documenting considerable gains provided by the proposed hierarchical approach.