Epidermal patterning in Arabidopsis: models make a difference

Stochastic Turing patterns of trichomes in Arabidopsis leaves

Biological patterns that emerge during the morphogenesis of multicellular organisms can display high precision at large scales, while at cellular scales, cells exhibit large fluctuations stemming from cell-cell differences in molecular copy numbers also called demographic noise. We study the conflicting interplay between high precision and demographic noise in trichome patterns on the epidermis of wild-type Arabidopsis thaliana leaves, as a two-dimensional model system. We carry out a statistical characterization of these patterns and show that their power spectra display fat tails-a signature compatible with noise-driven stochastic Turing patterns-which are absent in power spectra of patterns driven by deterministic instabilities. We then present a theoretical model that includes demographic noise stemming from birth-death processes of genetic regulators which we study analytically and by stochastic simulations. The model captures the observed experimental features of trichome patterns.

Repressors of anthocyanin biosynthesis

Anthocyanins play a variety of adaptive roles in both vegetative tissues and reproductive organs of plants. The broad functionality of these compounds requires sophisticated regulation of the anthocyanin biosynthesis pathway to allow proper localization, timing, and optimal intensity of pigment deposition. While it is well-established that the committed steps of anthocyanin biosynthesis are activated by a highly conserved MYB-bHLH-WDR (MBW) protein complex in virtually all flowering plants, anthocyanin repression seems to be achieved by a wide variety of protein and small RNA families that function in different tissue types and in response to different developmental, environmental, and hormonal cues. In this review, we survey recent progress in the identification of anthocyanin repressors and the characterization of their molecular mechanisms. We find that these seemingly very different repression modules act through a remarkably similar logic, the so-called 'double-negative logic'. Much of the double-negative regulation of anthocyanin production involves signal-induced degradation or sequestration of the repressors from the MBW protein complex. We discuss the functional and evolutionary advantages of this logic design compared with simple or sequential positive regulation. These advantages provide a plausible explanation as to why plants have evolved so many anthocyanin repressors.

Dynamical modules in metabolism, cell and developmental biology

Modularity is an essential feature of any adaptive complex system. Phenotypic traits are modules in the sense that they have a distinguishable structure or function, which can vary (quasi-)independently from its context. Since all phenotypic traits are the product of some underlying regulatory dynamics, the generative processes that constitute the genotype-phenotype map must also be functionally modular. Traditionally, modular processes have been identified as structural modules in regulatory networks. However, structure only constrains, but does not determine, the dynamics of a process. Here, we propose an alternative approach that decomposes the behaviour of a complex regulatory system into elementary activity-functions. Modular activities can occur in networks that show no structural modularity, making dynamical modularity more widely applicable than structural decomposition. Furthermore, the behaviour of a regulatory system closely mirrors its functional contribution to the outcome of a process, which makes dynamical modularity particularly suited for functional decomposition. We illustrate our approach with numerous examples from the study of metabolism, cellular processes, as well as development and pattern formation. We argue that dynamical modules provide a shared conceptual foundation for developmental and evolutionary biology, and serve as the foundation for a new account of process homology, which is presented in a separate contribution by DiFrisco and Jaeger to this focus issue.

Turing-like mechanism in a stochastic reaction-diffusion model recreates three dimensional vascular patterning of plant stems

Vascular tissue in plants provides a resource distribution network for water and nutrients that exhibits remarkable diversity in patterning among different species. In many succulent plants, the vascular network includes longitudinally-oriented supplemental vascular bundles (SVBs) in the central core of the succulent stems and roots in addition to the more typical zone of vascular tissue development (vascular cambium) in a cylinder at the periphery of the succulent organ. Plant SVBs evolved in over 38 plant families often in tandem with evolutionary increases in stem and root parenchyma storage tissue, so it is of interest to understand the evolutionary-developmental processes responsible for their recurrent evolution and patterning. Previous mathematical models have successfully recreated the two-dimensional vascular patterns in stem and root cross sections, but such models have yet to recreate three-dimensional vascular patterning. Here, a stochastic reaction-diffusion model of plant vascular bundle patterning is developed in an effort to highlight a potential mechanism of three dimensional patterning-Turing pattern formation coupled with longitudinal efflux of a regulatory molecule. A relatively simple model of four or five molecules recreated empirical SVB patterns and many other common vascular arrangements. SVBs failed to develop below a threshold width of parenchymatous tissues, suggesting a mechanism of evolutionary character loss due to changes in the spatial context in which development takes place. Altered diffusion rates of the modeled activator and substrate molecules affected the number and size of the simulated SVBs. This work provides a first mathematical model employing a stochastic Turing-type mechanism that recreates three dimensional vascular patterns seen in plant stems. The model offers predictions that can be tested using molecular-genetic approaches. Evolutionary-developmental ramifications concerning evolution of diffusion rates, organ size and geometry are discussed.

Modularity, criticality, and evolvability of a developmental gene regulatory network

The existence of discrete phenotypic traits suggests that the complex regulatory processes which produce them are functionally modular. These processes are usually represented by networks. Only modular networks can be partitioned into intelligible subcircuits able to evolve relatively independently. Traditionally, functional modularity is approximated by detection of modularity in network structure. However, the correlation between structure and function is loose. Many regulatory networks exhibit modular behaviour without structural modularity. Here we partition an experimentally tractable regulatory network-the gap gene system of dipteran insects-using an alternative approach. We show that this system, although not structurally modular, is composed of dynamical modules driving different aspects of whole-network behaviour. All these subcircuits share the same regulatory structure, but differ in components and sensitivity to regulatory interactions. Some subcircuits are in a state of criticality, while others are not, which explains the observed differential evolvability of the various expression features in the system.

Dynamical Patterning Modules, Biogeneric Materials, and the Evolution of Multicellular Plants

Comparative analyses of developmental processes across a broad spectrum of organisms are required to fully understand the mechanisms responsible for the major evolutionary transitions among eukaryotic photosynthetic lineages (defined here as the polyphyletic algae and the monophyletic land plants). The concepts of dynamical patterning modules (DPMs) and biogeneric materials provide a framework for studying developmental processes in the context of such comparative analyses. In the context of multicellularity, DPMs are defined as sets of conserved gene products and molecular networks, in conjunction with the physical morphogenetic and patterning processes they mobilize. A biogeneric material is defined as mesoscale matter with predictable morphogenetic capabilities that arise from complex cellular conglomerates. Using these concepts, we outline some of the main events and transitions in plant evolution, and describe the DPMs and biogeneric properties associated with and responsible for these transitions. We identify four primary DPMs that played critical roles in the evolution of multicellularity (i.e., the DPMs responsible for cell-to-cell adhesion, identifying the future cell wall, cell differentiation, and cell polarity). Three important conclusions emerge from a broad phyletic comparison: (1) DPMs have been achieved in different ways, even within the same clade (e.g., phycoplastic cell division in the Chlorophyta and phragmoplastic cell division in the Streptophyta), (2) DPMs had their origins in the co-option of molecular species present in the unicellular ancestors of multicellular plants, and (3) symplastic transport mediated by intercellular connections, particularly plasmodesmata, was critical for the evolution of complex multicellularity in plants.

The CD4+ T cell regulatory network mediates inflammatory responses during acute hyperinsulinemia: a simulation study

Background

Obesity is frequently linked to insulin resistance, high insulin levels, chronic inflammation, and alterations in the behaviour of CD4+ T cells. Despite the biomedical importance of this condition, the system-level mechanisms that alter CD4+ T cell differentiation and plasticity are not well understood.

Results

We model how hyperinsulinemia alters the dynamics of the CD4+ T regulatory network, and this, in turn, modulates cell differentiation and plasticity. Different polarizing microenvironments are simulated under basal and high levels of insulin to assess impacts on cell-fate attainment and robustness in response to transient perturbations. In the presence of high levels of insulin Th1 and Th17 become more stable to transient perturbations, and their basin sizes are augmented, Tr1 cells become less stable or disappear, while TGFβ producing cells remain unaltered. Hence, the model provides a dynamic system-level framework and explanation to further understand the documented and apparently paradoxical role of TGFβ in both inflammation and regulation of immune responses, as well as the emergence of the adipose Treg phenotype. Furthermore, our simulations provide new predictions on the impact of the microenvironment in the coexistence of the different cell types, suggesting that in pro-Th1, pro-Th2 and pro-Th17 environments effector and regulatory cells can coexist, but that high levels of insulin severely diminish regulatory cells, especially in a pro-Th17 environment.

Conclusions

This work provides a first step towards a system-level formal and dynamic framework to integrate further experimental data in the study of complex inflammatory diseases.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-017-0436-y) contains supplementary material, which is available to authorized users.

Integration of transcriptomic and proteomic analysis towards understanding the systems biology of root hairs

Plants and other multicellular organisms consist of many types of specialized cells. Systems-wide exploration of large-scale information from singe cell level is essential to understand how cell works. Root hairs, tubular-shaped outgrowths from root epidermal cells, play important roles in the acquisition of nutrients and water, in the interaction with microbe, and in plant anchorage, and represent an ideal model to study the biology of a single cell type. Single cell sampling combined with omics approaches has been applied to study plant root hairs. This review emphasizes the integration of omics approaches towards understanding the systems biology of root hairs, unraveling the common and plant species-specific properties of root hairs, as well as the concordance of protein and transcript abundance. Understanding plant root hair biology by mining the integrated omics data will provide a way to know how a single cell differentiates, elongates, and functions, which might help molecularly modify crops for developing sustainable agriculture practices.

A Model Analysis of Mechanisms for Radial Microtubular Patterns at Root Hair Initiation Sites

Plant cells have two main modes of growth generating anisotropic structures. Diffuse growth where whole cell walls extend in specific directions, guided by anisotropically positioned cellulose fibers, and tip growth, with inhomogeneous addition of new cell wall material at the tip of the structure. Cells are known to regulate these processes via molecular signals and the cytoskeleton. Mechanical stress has been proposed to provide an input to the positioning of the cellulose fibers via cortical microtubules in diffuse growth. In particular, a stress feedback model predicts a circumferential pattern of fibers surrounding apical tissues and growing primordia, guided by the anisotropic curvature in such tissues. In contrast, during the initiation of tip growing root hairs, a star-like radial pattern has recently been observed. Here, we use detailed finite element models to analyze how a change in mechanical properties at the root hair initiation site can lead to star-like stress patterns in order to understand whether a stress-based feedback model can also explain the microtubule patterns seen during root hair initiation. We show that two independent mechanisms, individually or combined, can be sufficient to generate radial patterns. In the first, new material is added locally at the position of the root hair. In the second, increased tension in the initiation area provides a mechanism. Finally, we describe how a molecular model of Rho-of-plant (ROP) GTPases activation driven by auxin can position a patch of activated ROP protein basally along a 2D root epidermal cell plasma membrane, paving the way for models where mechanical and molecular mechanisms cooperate in the initial placement and outgrowth of root hairs.

Development of cell differentiation in the transition to multicellularity: a dynamical modeling approach

Multicellularity has emerged and continues to emerge in a variety of lineages and under diverse environmental conditions. In order to attain individuality and integration, multicellular organisms must exhibit spatial cell differentiation, which in turn allows cell aggregates to robustly generate traits and behaviors at the multicellular level. Nevertheless, the mechanisms that may lead to the development of cellular differentiation and patterning in emerging multicellular organisms remain unclear. We briefly review two conceptual frameworks that have addressed this issue: the cooperation-defection framework and the dynamical patterning modules (DPMs) framework. Then, situating ourselves in the DPM formalism first put forward by S. A. Newman and collaborators, we state a hypothesis for cell differentiation and arrangement in cellular masses of emerging multicellular organisms. Our hypothesis is based on the role of the generic cell-to-cell communication and adhesion patterning mechanisms, which are two fundamental mechanisms for the evolution of multicellularity, and whose molecules seem to be well-conserved in extant multicellular organisms and their unicellular relatives. We review some fundamental ideas underlying this hypothesis and contrast them with empirical and theoretical evidence currently available. Next, we use a mathematical model to illustrate how the mechanisms and assumptions considered in the hypothesis we postulate may render stereotypical arrangements of differentiated cells in an emerging cellular aggregate and may contribute to the variation and recreation of multicellular phenotypes. Finally, we discuss the potential implications of our approach and compare them to those entailed by the cooperation-defection framework in the study of cell differentiation in the transition to multicellularity.

SABRE is required for stabilization of root hair patterning in Arabidopsis thaliana

Patterned differentiation of distinct cell types is essential for the development of multicellular organisms. The root epidermis of Arabidopsis thaliana is composed of alternating files of root hair and non-hair cells and represents a model system for studying the control of cell-fate acquisition. Epidermal cell fate is regulated by a network of genes that translate positional information from the underlying cortical cell layer into a specific pattern of differentiated cells. While much is known about the genes of this network, new players continue to be discovered. Here we show that the SABRE (SAB) gene, known to mediate microtubule organization, anisotropic cell growth and planar polarity, has an effect on root epidermal hair cell patterning. Loss of SAB function results in ectopic root hair formation and destabilizes the expression of cell fate and differentiation markers in the root epidermis, including expression of the WEREWOLF (WER) and GLABRA2 (GL2) genes. Double mutant analysis reveal that wer and caprice (cpc) mutants, defective in core components of the epidermal patterning pathway, genetically interact with sab. This suggests that SAB may act on epidermal patterning upstream of WER and CPC. Hence, we provide evidence for a role of SAB in root epidermal patterning by affecting cell-fate stabilization. Our work opens the door for future studies addressing SAB-dependent functions of the cytoskeleton during root epidermal patterning.

Root hairs

Roots hairs are cylindrical extensions of root epidermal cells that are important for acquisition of nutrients, microbe interactions, and plant anchorage. The molecular mechanisms involved in the specification, differentiation, and physiology of root hairs in Arabidopsis are reviewed here. Root hair specification in Arabidopsis is determined by position-dependent signaling and molecular feedback loops causing differential accumulation of a WD-bHLH-Myb transcriptional complex. The initiation of root hairs is dependent on the RHD6 bHLH gene family and auxin to define the site of outgrowth. Root hair elongation relies on polarized cell expansion at the growing tip, which involves multiple integrated processes including cell secretion, endomembrane trafficking, cytoskeletal organization, and cell wall modifications. The study of root hair biology in Arabidopsis has provided a model cell type for insights into many aspects of plant development and cell biology.

Quantification of variability in trichome patterns

While pattern formation is studied in various areas of biology, little is known about the noise leading to variations between individual realizations of the pattern. One prominent example for de novo pattern formation in plants is the patterning of trichomes on Arabidopsis leaves, which involves genetic regulation and cell-to-cell communication. These processes are potentially variable due to, e.g., the abundance of cell components or environmental conditions. To elevate the understanding of regulatory processes underlying the pattern formation it is crucial to quantitatively analyze the variability in naturally occurring patterns. Here, we review recent approaches toward characterization of noise on trichome initiation. We present methods for the quantification of spatial patterns, which are the basis for data-driven mathematical modeling and enable the analysis of noise from different sources. Besides the insight gained on trichome formation, the examination of observed trichome patterns also shows that highly regulated biological processes can be substantially affected by variability.

Dynamic models of epidermal patterning as an approach to plant eco-evo-devo

Epidermal patterning in Arabidopsis thaliana leaves and root has become a model system for experimental and theoretical developmental studies, yielding well-characterized regulatory networks. We succinctly review the dynamic models proposed for this system and then argue that it provides an excellent instance to integrate and further study the role of non-genetic factors in plant development and evolution. Then, we set up to review the role of phytohormones and environmental stimuli in the regulation of cell-fate determination and patterning in this system. We conclude that dynamic modeling of complex regulatory networks can help understand the plasticity and variability of cellular patterns, and hence, such modeling approaches can be expanded to advance in the consolidation of plant Evolutionary and Ecological Developmental Biology (eco-evo-devo).

When and where plant cells divide: a perspective from computational modeling

Computational modeling of growing plant tissues raises two basic questions about plant cell division: when does a cell decide to divide and where is the new wall placed? Although biologists and modelers commonly assume that a cell divides after it reaches a threshold size, two recent experiments show that models with variable division sizes better replicate the tissue. Similarly, comparing model predictions with living plant cells reveals that the choice of division plane is variable, although the shortest path dividing a cell in half (i.e. the minimal surface area) is the most probable division plane.

From landing lights to mimicry: the molecular regulation of flower colouration and mechanisms for pigmentation patterning

Flower colour is a key component for plant signaling to pollinators and a staggering variety of colour variations are found in nature. Patterning of flower colour, such as pigment spots or stripes, is common and is important in promoting pollination success. Developmentally programmed pigmentation patterns are of interest with respect to the evolution of specialised plant-pollinator associations and as models for dissecting regulatory signaling in plants. This article reviews the occurrence and function of flower colour patterns, as well as the molecular genetics of anthocyanin pigmentation regulation. The transcription factors controlling anthocyanin biosynthesis have been characterised for many species and an 'MBW' regulatory complex of R2R3MYB, bHLH and WD-Repeat proteins is of central importance. In particular, R2R3MYBs are key determinants of pigmentation intensity and patterning in plants. Progress is now being made on how environmental or developmental signal pathways may in turn control the production of the MBW components. Furthermore, additional regulatory proteins that interact with the MBW activation complex are being identified, including a range of proteins that repress complex formation or action, either directly or indirectly. This review discusses some of the recent data on the regulatory factors and presents models of how patterns may be determined.

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.

Dynamic network-based epistasis analysis: boolean examples

In this article we focus on how the hierarchical and single-path assumptions of epistasis analysis can bias the inference of gene regulatory networks. Here we emphasize the critical importance of dynamic analyses, and specifically illustrate the use of Boolean network models. Epistasis in a broad sense refers to gene interactions, however, as originally proposed by Bateson, epistasis is defined as the blocking of a particular allelic effect due to the effect of another allele at a different locus (herein, classical epistasis). Classical epistasis analysis has proven powerful and useful, allowing researchers to infer and assign directionality to gene interactions. As larger data sets are becoming available, the analysis of classical epistasis is being complemented with computer science tools and system biology approaches. We show that when the hierarchical and single-path assumptions are not met in classical epistasis analysis, the access to relevant information and the correct inference of gene interaction topologies is hindered, and it becomes necessary to consider the temporal dynamics of gene interactions. The use of dynamical networks can overcome these limitations. We particularly focus on the use of Boolean networks that, like classical epistasis analysis, relies on logical formalisms, and hence can complement classical epistasis analysis and relax its assumptions. We develop a couple of theoretical examples and analyze them from a dynamic Boolean network model perspective. Boolean networks could help to guide additional experiments and discern among alternative regulatory schemes that would be impossible or difficult to infer without the elimination of these assumption from the classical epistasis analysis. We also use examples from the literature to show how a Boolean network-based approach has resolved ambiguities and guided epistasis analysis. Our article complements previous accounts, not only by focusing on the implications of the hierarchical and single-path assumption, but also by demonstrating the importance of considering temporal dynamics, and specifically introducing the usefulness of Boolean network models and also reviewing some key properties of network approaches.

Progress on trichome development regulated by phytohormone signaling

Trichomes are specialized structures that develop from epidermal cells in the aerial parts of plants, and are an excellent model system to study all aspects of cell differentiation including cell fate determination, cell cycle regulation, cell polarity and cell expansion. The development of the trichome is a process of integration of both external signals and endogenous developmental programs. During recent years, molecular analysis of trichome development at different stages has been well studied, and through the mutant phenotypes and the function of corresponding genes, the underlying mechanism has been revealed in a first glimpse. This paper offers a mini-view on this integration process with emphasis on the effects of plant hormone signaling on trichome development in plants through GLABROUS INFLORESCENCE STEMS (GIS) family and subfamily genes.