Cell patterns emerge from coupled chemical and physical fields with cell proliferation dynamics: the Arabidopsis thaliana root as a study system

Application of Green-enhanced Nano-lantern as a bioluminescent ratiometric indicator for measurement of Arabidopsis thaliana root apoplastic fluid pH

Plant root absorbs water and nutrients from the soil, and the root apoplastic fluid (AF) is an important intermediate between cells and the surrounding environment. The acid growth theory suggests that an acidic AF is needed for cell wall expansion during root growth. However, technical limitations have precluded the quantification of root apoplastic fluid pH (AF-pH). Here, we used Green-enhanced Nano-lantern (GeNL), a chimeric protein of the luciferase NanoLuc (Nluc) and the green fluorescent protein mNeonGreen (mNG), as a ratiometric pH indicator based on the pH dependency of bioluminescence resonance energy transfer efficiency from Nluc to mNG. Luminescence spectrum of GeNL changed reciprocally from pH 4.5 to 7.5, with a pK_a of 5.5. By fusing GeNL to a novel signal peptide from Arabidopsis thaliana Cellulase 1, we localised GeNL in A. thaliana AF. We visualised AF dynamics at subcellular resolution over 30 min and determined flow velocity in the maturation zone to be 0.97± 0.06 μm/s. We confirmed that the developing root AF is acidic in the pH range of 5.1-5.7, suggesting that the AF-pH is tightly regulated during root elongation. These results support the acid growth theory and provide evidence for AF-pH maintenance despite changes in ambient pH.

Gene Regulatory Network Dynamical Logical Models for Plant Development

Mathematical and computational approaches that integrate and model the concerted action of multiple genetic and nongenetic components holding highly nonlinear interactions are fundamental for the study of developmental processes. Among these, gene regulatory network (GRN) dynamical models are very useful to understand how diverse types of regulatory constraints restrict the multigene expression patterns that characterize different cell fates. In this chapter we present a hands-on approach to model GRN dynamics, taking as a working example a well-curated and experimentally grounded GRN developmental module proposed by our group: the flower organ specification gene regulatory network (FOS-GRN). We demonstrate how to build and analyze a GRN model according to the following steps: (1) integration of molecular genetic data and formulation of logical rules specifying the dynamic behavior of each gene; (2) determination of steady states (attractors) corresponding to each cell type; (3) validation of the GRN model; and (4) extension of the deterministic model with the inclusion of stochasticity in order to model cell-state transitions dependent on noise due to fluctuations of the involved gen products. The methodologies explained here in detail can be applied to any other developmental module.

A Sight on Single-Cell Transcriptomics in Plants Through the Prism of Cell-Based Computational Modeling Approaches: Benefits and Challenges for Data Analysis

Single-cell technology is a relatively new and promising way to obtain high-resolution transcriptomic data mostly used for animals during the last decade. However, several scientific groups developed and applied the protocols for some plant tissues. Together with deeply-developed cell-resolution imaging techniques, this achievement opens up new horizons for studying the complex mechanisms of plant tissue architecture formation. While the opportunities for integrating data from transcriptomic to morphogenetic levels in a unified system still present several difficulties, plant tissues have some additional peculiarities. One of the plants' features is that cell-to-cell communication topology through plasmodesmata forms during tissue growth and morphogenesis and results in mutual regulation of expression between neighboring cells affecting internal processes and cell domain development. Undoubtedly, we must take this fact into account when analyzing single-cell transcriptomic data. Cell-based computational modeling approaches successfully used in plant morphogenesis studies promise to be an efficient way to summarize such novel multiscale data. The inverse problem's solutions for these models computed on the real tissue templates can shed light on the restoration of individual cells' spatial localization in the initial plant organ-one of the most ambiguous and challenging stages in single-cell transcriptomic data analysis. This review summarizes new opportunities for advanced plant morphogenesis models, which become possible thanks to single-cell transcriptome data. Besides, we show the prospects of microscopy and cell-resolution imaging techniques to solve several spatial problems in single-cell transcriptomic data analysis and enhance the hybrid modeling framework opportunities.

Information Processing in the Brain as Optimal Entropy Transport: A Theoretical Approach

We consider brain activity from an information theoretic perspective. We analyze the information processing in the brain, considering the optimality of Shannon entropy transport using the Monge–Kantorovich framework. It is proposed that some of these processes satisfy an optimal transport of informational entropy condition. This optimality condition allows us to derive an equation of the Monge–Ampère type for the information flow that accounts for the branching structure of neurons via the linearization of this equation. Based on this fact, we discuss a version of Murray’s law in this context.

The recent advances in the mathematical modelling of human pluripotent stem cells

Human pluripotent stem cells hold great promise for developments in regenerative medicine and drug design. The mathematical modelling of stem cells and their properties is necessary to understand and quantify key behaviours and develop non-invasive prognostic modelling tools to assist in the optimisation of laboratory experiments. Here, the recent advances in the mathematical modelling of hPSCs are discussed, including cell kinematics, cell proliferation and colony formation, and pluripotency and differentiation.

Natural Root Cellular Variation in Responses to Osmotic Stress in Arabidopsis thaliana Accessions

Arabidopsis naturally occurring populations have allowed for the identification of considerable genetic variation remodeled by adaptation to different environments and stress conditions. Water is a key resource that limits plant growth, and its availability is initially sensed by root tissues. The root’s ability to adjust its physiology and morphology under water deficit makes this organ a useful model to understand how plants respond to water stress. Here, we used hyperosmotic shock stress treatments in different Arabidopsis accessions to analyze the root cell morphological responses. We found that osmotic stress conditions reduced root growth and root apical meristem (RAM) size, promoting premature cell differentiation without affecting the stem cell niche morphology. This phenotype was accompanied by a cluster of small epidermal and cortex cells with radial expansion and root hairs at the transition to the elongation zone. We also found this radial expansion with root hairs when plants are grown under hypoosmotic conditions. Finally, root growth was less affected by osmotic stress in the Sg-2 accession followed by Ws, Cvi-0, and Col-0; however, after a strong osmotic stress, Sg-2 and Cvi-0 were the most resilience accessions. The sensitivity differences among these accessions were not explained by stress-related gene expression. This work provides new cellular insights on the Arabidopsis root phenotypic variability and plasticity to osmotic stress.

MADS-box genes underground becoming mainstream: plant root developmental mechanisms

Plant growth is largely post-embryonic and depends on meristems that are active throughout the lifespan of an individual. Developmental patterns rely on the coordinated spatio-temporal expression of different genes, and the activity of transcription factors is particularly important during most morphogenetic processes. MADS-box genes constitute a transcription factor family in eukaryotes. In Arabidopsis, their proteins participate in all major aspects of shoot development, but their role in root development is still not well characterized. In this review we synthetize current knowledge pertaining to the function of MADS-box genes highly expressed in roots: XAL1, XAL2, ANR1 and AGL21, as well as available data for other MADS-box genes expressed in this organ. The role of Trithorax group and Polycomb group complexes on MADS-box genes' epigenetic regulation is also discussed. We argue that understanding the role of MADS-box genes in root development of species with contrasting architectures is still a challenge. Finally, we propose that MADS-box genes are key components of the gene regulatory networks that underlie various gene expression patterns, each one associated with the distinct developmental fates observed in the root. In the case of XAL1 and XAL2, their role within these networks could be mediated by regulatory feedbacks with auxin.

Coherent directed movement toward food modeled in Trichoplax, a ciliated animal lacking a nervous system

Trichoplax adhaerens is a small, ciliated marine animal that glides on surfaces grazing upon algae, which it digests externally. It has no muscles or nervous system and only six cell types, all but two of which are embedded in its epithelium. The epithelial cells are joined by apical adherens junctions; neither tight junctions nor gap junctions are present. Monociliated epithelial cells on the lower surface propel gliding. The cilia beat regularly, but asynchronously, and transiently contact the substrate with each stroke. The animal moves in random directions in the absence of food. We show here that it exhibits chemotaxis, moving preferentially toward algae embedded in a disk of agar. We present a mathematical model to explain how coherent, directional movements could arise from the collective actions of a set of ciliated epithelial cells, each independently sensing and responding to a chemoattractant gradient. The model incorporates realistic values for viscoelastic properties of cells and produces coordinated movements and changes in body shape that resemble the actual movements of the animal. The model demonstrates that an animal can move coherently in search of food without any need for chemical signaling between cells and introduces a different approach to modeling behavior in primitive multicellular organisms.

Algorithm for a particle-based growth model for plant tissues

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

Curvature-driven spatial patterns in growing 3D domains: A mechanochemical model for phyllotaxis

Here we discuss the formation of phyllotactic patterns in the shoot apical meristem (SAM) of plants, where the spatial distribution of the phytohormone auxin determines phyllotaxis in a domain that is growing and changing in time. We assume that the concentration of auxin modifies the mechanical properties of the domain and that the mechanical stress field in the SAM orients the flux of auxin. To study this problem we propose a mechanism for pattern formation in growing domains with variable curvature. The dynamics of chemicals is modeled by a reaction-diffusion system that produces a three dimensional pattern of chemical concentrations that changes the stress field in the domain while growing. The growth process is modeled by a phase-field order parameter which determines the location of the boundaries of the domain. This field is coupled to the chemical concentration through a curvature term that affects the local mechanical stress in the domain. The local stress changes in turn modify the chemical patterns. Our model constitutes a useful and novel approach in theoretical biology, as many developmental processes in organisms seem to be affected by the changes of curvature, size, mechanical stress and other physical aspects. Several patterns seen in many plants are reproduced under certain conditions by our model.

Medical Systems Biology

The aim of this volume is to encourage the use of systems-level methodologies to contribute to the improvement of human-health . We intend to motivate biomedical researchers to complement their current theoretical and empirical practice with up-to-date systems biology conceptual approaches. Our perspective is based on the deep understanding of the key biomolecular regulatory mechanisms that underlie health, as well as the emergence and progression of human-disease . We strongly believe that the contemporary systems biology perspective opens the door to the effective development of novel methodologies to the improvement of prevention . This requires a deeper and integrative understanding of the involved underlying systems-level mechanisms. In order to explain our proposal in a simple way, in this chapter we privilege the conceptual exposition of our chosen framework over formal considerations. The formal exposition of our proposal will be expanded and discussed later in the next chapters.

A physico-genetic module for the polarisation of auxin efflux carriers PIN-FORMED (PIN)

Intracellular polarisation of auxin efflux carriers is crucial for understanding how auxin gradients form in plants. The polarisation dynamics of auxin efflux carriers PIN-FORMED (PIN) depends on both biomechanical forces as well as chemical, molecular and genetic factors. Biomechanical forces have shown to affect the localisation of PIN transporters to the plasma membrane. We propose a physico-genetic module of PIN polarisation that integrates biomechanical, molecular, and cellular processes as well as their non-linear interactions. The module was implemented as a discrete Boolean model and then approximated to a continuous dynamic system, in order to explore the relative contribution of the factors mediating PIN polarisation at the scale of single cell. Our models recovered qualitative behaviours that have been experimentally observed and enable us to predict that, in the context of PIN polarisation, the effects of the mechanical forces can predominate over the activity of molecular factors such as the GTPase ROP6 and the ROP-INTERACTIVE CRIB MOTIF-CONTAINING PROTEIN RIC1.

Identifying the transition to the maturation zone in three ecotypes of Arabidopsis thaliana roots

The Arabidopsis thaliana (hereafter Arabidopsis) root has become a useful model for studying how organ morphogenesis emerge from the coordination and balance of cell proliferation and differentiation, as both processes may be observed and quantified in the root at different stages of development. Hence, being able to objectively identify and delimit the different stages of root development has been very important. Up to now, three different zones along the longitudinal axis of the primary root of Arabidopsis, have been identified: the root apical meristematic zone (RAM) with two domains [the proliferative (PD) and the transition domain (TD)], the elongation zone (EZ) and the maturation zone (MZ). We previously reported a method to quantify the length of the cells of the meristematic and the elongation zone, as well as the boundaries or transitions between the root domains along the growing part of the Arabidopsis root. In this study, we provide a more accurate criterion to identify the MZ. Traditionally, the transition between the EZ to the MZ has been established by the emergence of the first root-hair bulge in the epidermis, because this emergence coincides with cell maturation in this cell type. But we have found here that after the emergence of the first root-hair bulge some cells continue to elongate and we have confirmed this in three different Arabidopsis ecotypes. We established the limit between the EZ and the MZ by looking for the closest cortical cell with a longer length than the average cell length of 10 cells after the cortical cell closest to the epidermal cell with the first root-hair bulge in these three ecotypes. In Col-0 and Ws this cell is four cells above the one with the root hair bulge and, in the Ler ecotype, this cell is five cells above. To unambiguously identifying the site at which cells stop elongating and attain their final length and fate at the MZ, we propose to calculate the length of completely elongated cortical cells counting 10 cells starting from the sixth cell above the cortical cell closest to the epidermal cell with the first root-hair bulge. We validated this proposal in the three ecotypes analyzed and consider that this proposal may aid at having a more objective way to characterize root phenotypes and compare among them.

A hybrid computational model to explore the topological characteristics of epithelial tissues

Epithelial tissues show a particular topology where cells resemble a polygon-like shape, but some biological processes can alter this tissue topology. During cell proliferation, mitotic cell dilation deforms the tissue and modifies the tissue topology. Additionally, cells are reorganized in the epithelial layer and these rearrangements also alter the polygon distribution. We present here a computer-based hybrid framework focused on the simulation of epithelial layer dynamics that combines discrete and continuum numerical models. In this framework, we consider topological and mechanical aspects of the epithelial tissue. Individual cells in the tissue are simulated by an off-lattice agent-based model, which keeps the information of each cell. In addition, we model the cell-cell interaction forces and the cell cycle. Otherwise, we simulate the passive mechanical behaviour of the cell monolayer using a material that approximates the mechanical properties of the cell. This continuum approach is solved by the finite element method, which uses a dynamic mesh generated by the triangulation of cell polygons. Forces generated by cell-cell interaction in the agent-based model are also applied on the finite element mesh. Cell movement in the agent-based model is driven by the displacements obtained from the deformed finite element mesh of the continuum mechanical approach. We successfully compare the results of our simulations with some experiments about the topology of proliferating epithelial tissues in Drosophila. Our framework is able to model the emergent behaviour of the cell monolayer that is due to local cell-cell interactions, which have a direct influence on the dynamics of the epithelial tissue.

Identifying Developmental Zones in Maize Lateral Root Cell Length Profiles using Multiple Change-Point Models

The identification of the limits between the cell division, elongation and mature zones in the root apex is still a matter of controversy when methods based on cellular features, molecular markers or kinematics are compared while methods based on cell length profiles have been comparatively underexplored. Segmentation models were developed to identify developmental zones within a root apex on the basis of epidermal cell length profiles. Heteroscedastic piecewise linear models were estimated for maize lateral roots of various lengths of both wild type and two mutants affected in auxin signaling (rtcs and rum-1). The outputs of these individual root analyses combined with morphological features (first root hair position and root diameter) were then globally analyzed using principal component analysis. Three zones corresponding to the division zone, the elongation zone and the mature zone were identified in most lateral roots while division zone and sometimes elongation zone were missing in arrested roots. Our results are consistent with an auxin-dependent coordination between cell flux, cell elongation and cell differentiation. The proposed segmentation models could extend our knowledge of developmental regulations in longitudinally organized plant organs such as roots, monocot leaves or internodes.

A dynamic genetic-hormonal regulatory network model explains multiple cellular behaviors of the root apical meristem of Arabidopsis thaliana

The study of the concerted action of hormones and transcription factors is fundamental to understand cell differentiation and pattern formation during organ development. The root apical meristem of Arabidopsis thaliana is a useful model to address this. It has a stem cell niche near its tip conformed of a quiescent organizer and stem or initial cells around it, then a proliferation domain followed by a transition domain, where cells diminish division rate before transiting to the elongation zone; here, cells grow anisotropically prior to their final differentiation towards the plant base. A minimal model of the gene regulatory network that underlies cell-fate specification and patterning at the root stem cell niche was proposed before. In this study, we update and couple such network with both the auxin and cytokinin hormone signaling pathways to address how they collectively give rise to attractors that correspond to the genetic and hormonal activity profiles that are characteristic of different cell types along A. thaliana root apical meristem. We used a Boolean model of the genetic-hormonal regulatory network to integrate known and predicted regulatory interactions into alternative models. Our analyses show that, after adding some putative missing interactions, the model includes the necessary and sufficient components and regulatory interactions to recover attractors characteristic of the root cell types, including the auxin and cytokinin activity profiles that correlate with different cellular behaviors along the root apical meristem. Furthermore, the model predicts the existence of activity configurations that could correspond to the transition domain. The model also provides a possible explanation for apparently paradoxical cellular behaviors in the root meristem. For example, how auxin may induce and at the same time inhibit WOX5 expression. According to the model proposed here the hormonal regulation of WOX5 might depend on the cell type. Our results illustrate how non-linear multi-stable qualitative network models can aid at understanding how transcriptional regulators and hormonal signaling pathways are dynamically coupled and may underlie both the acquisition of cell fate and the emergence of hormonal activity profiles that arise during complex organ development.

Model of polar auxin transport coupled to mechanical forces retrieves robust morphogenesis along the Arabidopsis root

Stem cells are identical in many scales, they share the same molecular composition, DNA, genes, and genetic networks, yet they should acquire different properties to form a functional tissue. Therefore, they must interact and get some external information from their environment, either spatial (dynamical fields) or temporal (lineage). In this paper we test to what extent coupled chemical and physical fields can underlie the cell's positional information during development. We choose the root apical meristem of Arabidopsis thaliana to model the emergence of cellular patterns. We built a model to study the dynamics and interactions between the cell divisions, the local auxin concentration, and physical elastic fields. Our model recovers important aspects of the self-organized and resilient behavior of the observed cellular patterns in the Arabidopsis root, in particular, the reverse fountain pattern observed in the auxin transport, the PIN-FORMED (protein family of auxin transporters) polarization pattern and the accumulation of auxin near the region of maximum curvature in a bent root. Our model may be extended to predict altered cellular patterns that are expected under various applied auxin treatments or modified physical growth conditions.

Computational Modeling of Auxin: A Foundation for Plant Engineering

Since the development of agriculture, humans have relied on the cultivation of plants to satisfy our increasing demand for food, natural products, and other raw materials. As we understand more about plant development, we can better manipulate plants to fulfill our particular needs. Auxins are a class of simple metabolites that coordinate many developmental activities like growth and the appearance of functional structures in plants. Computational modeling of auxin has proven to be an excellent tool in elucidating many mechanisms that underlie these developmental events. Due to the complexity of these mechanisms, current modeling efforts are concerned only with single phenomena focused on narrow spatial and developmental contexts; but a general model of plant development could be assembled by integrating the insights from all of them. In this perspective, we summarize the current collection of auxin-driven computational models, focusing on how they could come together into a single model for plant development. A model of this nature would allow researchers to test hypotheses in silico and yield accurate predictions about the behavior of a plant under a given set of physical and biochemical constraints. It would also provide a solid foundation toward the establishment of plant engineering, a proposed discipline intended to enable the design and production of plants that exhibit an arbitrarily defined set of features.

Spheroid Formation of Hepatocarcinoma Cells in Microwells: Experiments and Monte Carlo Simulations

The formation of spherical aggregates during the growth of cell population has long been observed under various conditions. We observed the formation of such aggregates during proliferation of Huh-7.5 cells, a human hepatocarcinoma cell line, in a microfabricated low-adhesion microwell system (SpheroFilm; formed of mass-producible silicone elastomer) on the length scales up to 500 μm. The cell proliferation was also tracked with immunofluorescence staining of F-actin and cell proliferation marker Ki-67. Meanwhile, our complementary 3D Monte Carlo simulations, taking cell diffusion and division, cell-cell and cell-scaffold adhesion, and gravity into account, illustrate the role of these factors in the formation of spheroids. Taken together, our experimental and simulation results provide an integrative view of the process of spheroid formation for Huh-7.5 cells.

Evolutionary Developmental Biology (Evo-Devo) Research in Latin America

Famous for its blind cavefish and Darwin's finches, Latin America is home to some of the richest biodiversity hotspots of our planet. The Latin American fauna and flora inspired and captivated naturalists from the nineteenth and twentieth centuries, including such notable pioneers such as Fritz Müller, Florentino Ameghino, and Léon Croizat who made a significant contribution to the study of embryology and evolutionary thinking. But, what are the historical and present contributions of the Latin American scientific community to Evo-Devo? Here, we provide the first comprehensive overview of the Evo-Devo laboratories based in Latin America and describe current lines of research based on endemic species, focusing on body plans and patterning, systematics, physiology, computational modeling approaches, ecology, and domestication. Literature searches reveal that Evo-Devo in Latin America is still in its early days; while showing encouraging indicators of productivity, it has not stabilized yet, because it relies on few and sparsely distributed laboratories. Coping with the rapid changes in national scientific policies and contributing to solve social and health issues specific to each region are among the main challenges faced by Latin American researchers. The 2015 inaugural meeting of the Pan-American Society for Evolutionary Developmental Biology played a pivotal role in bringing together Latin American researchers eager to initiate and consolidate regional and worldwide collaborative networks. Such networks will undoubtedly advance research on the extremely high genetic and phenotypic biodiversity of Latin America, bound to be an almost infinite source of amazement and fascinating findings for the Evo-Devo community.

Wide and high resolution tension measurement using FRET in embryo

During embryonic development, physical force plays an important role in morphogenesis and differentiation. Stretch sensitive fluorescence resonance energy transfer (FRET) has the potential to provide non-invasive tension measurements inside living tissue. In this study, we introduced a FRET-based actinin tension sensor into Xenopus laevis embryos and demonstrated that this sensor captures variation of tension across differentiating ectoderm. The actinin tension sensor, containing mCherry and EGFP connected by spider silk protein, was validated in human embryonic kidney (HEK) cells and embryos. It co-localized with actin filaments and changed FRET efficiencies in response to actin filament destruction, myosin deactivation, and osmotic perturbation. Time-lapse FRET analysis showed that the prospective neural ectoderm bears higher tension than the epidermal ectoderm during gastrulation and neurulation, and cells morphogenetic behavior correlated with the tension difference. These data confirmed that the sensor enables us to measure tension across tissues concurrently and with high resolution.

Dynamic network modelling to understand flowering transition and floral patterning

Differentiation and morphogenetic processes during plant development are particularly robust. At the cellular level, however, plants also show great plasticity in response to environmental conditions, and can even reverse apparently terminal differentiated states with remarkable ease. Can we understand and predict both robust and plastic systemic responses as a general consequence of the non-trivial interplay between intracellular regulatory networks, extrinsic environmental signalling, and tissue-level mechanical constraints? Flower development has become an ideal model system to study these general questions of developmental biology, which are especially relevant to understanding stem cell patterning in plants, animals, and human disease. Decades of detailed study of molecular developmental genetics, as well as novel experimental techniques for in vivo assays in both wild-type and mutant plants, enable the postulation and testing of experimentally grounded mathematical and computational network dynamical models. Research in our group aims to explain the emergence of robust transitions that occur at the shoot apical meristem, as well as flower development, as the result of the collective action of key molecular components in regulatory networks subjected to intra-organismal signalling and extracellular constraints. Here we present a brief overview of recent work from our group, and that of others, focusing on the use of simple dynamical models to address cell-fate specification and cell-state stochastic dynamics during flowering transition and cell-state transitions at the shoot apical meristem of Arabidopsis thaliana. We also focus on how our work fits within the general field of plant developmental modelling, which is being developed by many others.

Modeling plant development: from signals to gene networks

Mathematical modeling has become a common tool in plant developmental biology. Indeed, it allows for the prediction of complex and often unintuitive dynamics of the molecular networks driving plant development. This has enabled the test of their possible involvement in robust and specific developmental processes. Modeling has also been fruitful in predicting new interactions within gene networks, such as the Arabidopsis circadian clock. A new challenge is to integrate patterning issues with tissue growth and biomechanics. The development of new tools to gain resolution in data collection as well as new frameworks to confront models and data might provide even more robust predictions.

A Dynamic Gene Regulatory Network Model That Recovers the Cyclic Behavior of Arabidopsis thaliana Cell Cycle

Cell cycle control is fundamental in eukaryotic development. Several modeling efforts have been used to integrate the complex network of interacting molecular components involved in cell cycle dynamics. In this paper, we aimed at recovering the regulatory logic upstream of previously known components of cell cycle control, with the aim of understanding the mechanisms underlying the emergence of the cyclic behavior of such components. We focus on Arabidopsis thaliana, but given that many components of cell cycle regulation are conserved among eukaryotes, when experimental data for this system was not available, we considered experimental results from yeast and animal systems. We are proposing a Boolean gene regulatory network (GRN) that converges into only one robust limit cycle attractor that closely resembles the cyclic behavior of the key cell-cycle molecular components and other regulators considered here. We validate the model by comparing our in silico configurations with data from loss- and gain-of-function mutants, where the endocyclic behavior also was recovered. Additionally, we approximate a continuous model and recovered the temporal periodic expression profiles of the cell-cycle molecular components involved, thus suggesting that the single limit cycle attractor recovered with the Boolean model is not an artifact of its discrete and synchronous nature, but rather an emergent consequence of the inherent characteristics of the regulatory logic proposed here. This dynamical model, hence provides a novel theoretical framework to address cell cycle regulation in plants, and it can also be used to propose novel predictions regarding cell cycle regulation in other eukaryotes.

In multicellular organisms, cells undergo a cyclic behavior of DNA duplication and delivery of a copy to daughter cells during cell division. In each of the main cell-cycle (CC) stages different sets of proteins are active and genes are expressed. Understanding how such cycling cellular behavior emerges and is robustly maintained in the face of changing developmental and environmental conditions, remains a fundamental challenge of biology. The molecular components that cycle through DNA duplication and citokinesis are interconnected in a complex regulatory network. Several models of such network have been proposed, although the regulatory network that robustly recovers a limit-cycle steady state that resembles the behavior of CC molecular components has been recovered only in a few cases, and no comprehensive model exists for plants. In this paper we used the plant Arabidopsis thaliana, as a study system to propose a core regulatory network to recover a cyclic attractor that mimics the oscillatory behavior of the key CC components. Our analyses show that the proposed GRN model is robust to transient alterations, and is validated with the loss- and gain-of-function mutants of the CC components. The interactions proposed for Arabidopsis thaliana CC can inspire predictions for further uncovering regulatory motifs in the CC of other organisms including human.

Coherent motions in confluent cell monolayer sheets

Cell migration plays a pivotal role in many physiologically important processes such as embryogenesis, wound-healing, immune defense, and cancer metastasis. Although much effort has been directed toward motility of individual cells, the mechanisms underpinning collective cell migration remain poorly understood. Here we develop a collective motility model that incorporates cell mechanics and persistent random motions of individual cells to study coherent migratory motions in epithelial-like monolayers. This model, in absence of any external chemical signals, is able to explain coordinate rotational motion seen in systems ranging from two adherent cells to multicellular assemblies. We show that the competition between the active persistent force and random polarization fluctuation is responsible for the robust rotation. Passive mechanical coupling between cells is necessary but active chemical signaling between cells is not. The predicted angular motions also depend on the geometrical shape of the underlying substrate: cells exhibit collective rotation on circular substrates, but display linear back-and-forth motion on long and narrow substrates.

Modeling the epigenetic attractors landscape: toward a post-genomic mechanistic understanding of development

Robust temporal and spatial patterns of cell types emerge in the course of normal development in multicellular organisms. The onset of degenerative diseases may result from altered cell fate decisions that give rise to pathological phenotypes. Complex networks of genetic and non-genetic components underlie such normal and altered morphogenetic patterns. Here we focus on the networks of regulatory interactions involved in cell-fate decisions. Such networks modeled as dynamical non-linear systems attain particular stable configurations on gene activity that have been interpreted as cell-fate states. The network structure also restricts the most probable transition patterns among such states. The so-called Epigenetic Landscape (EL), originally proposed by C. H. Waddington, was an early attempt to conceptually explain the emergence of developmental choices as the result of intrinsic constraints (regulatory interactions) shaped during evolution. Thanks to the wealth of molecular genetic and genomic studies, we are now able to postulate gene regulatory networks (GRN) grounded on experimental data, and to derive EL models for specific cases. This, in turn, has motivated several mathematical and computational modeling approaches inspired by the EL concept, that may be useful tools to understand and predict cell-fate decisions and emerging patterns. In order to distinguish between the classical metaphorical EL proposal of Waddington, we refer to the Epigenetic Attractors Landscape (EAL), a proposal that is formally framed in the context of GRNs and dynamical systems theory. In this review we discuss recent EAL modeling strategies, their conceptual basis and their application in studying the emergence of both normal and pathological developmental processes. In addition, we discuss how model predictions can shed light into rational strategies for cell fate regulation, and we point to challenges ahead.

Role of transcriptional regulation in the evolution of plant phenotype: A dynamic systems approach

A growing body of evidence suggests that alterations in transcriptional regulation of genes involved in modulating development are an important part of phenotypic evolution, and this can be documented among species and within populations. While the effects of differential transcriptional regulation in organismal development have been preferentially studied in animal systems, this phenomenon has also been addressed in plants. In this review, we summarize evidence for cis-regulatory mutations, trans-regulatory changes and epigenetic modifications as molecular events underlying important phenotypic alterations, and thus shaping the evolution of plant development. We postulate that a mechanistic understanding of why such molecular alterations have a key role in development, morphology and evolution will have to rely on dynamic models of complex regulatory networks that consider the concerted action of genetic and nongenetic components, and that also incorporate the restrictions underlying the genotype to phenotype mapping process. Developmental Dynamics 244:1074-1095, 2015. © 2015 Wiley Periodicals, Inc.

Descriptive vs. mechanistic network models in plant development in the post-genomic era

Network modeling is now a widespread practice in systems biology, as well as in integrative genomics, and it constitutes a rich and diverse scientific research field. A conceptually clear understanding of the reasoning behind the main existing modeling approaches, and their associated technical terminologies, is required to avoid confusions and accelerate the transition towards an undeniable necessary more quantitative, multidisciplinary approach to biology. Herein, we focus on two main network-based modeling approaches that are commonly used depending on the information available and the intended goals: inference-based methods and system dynamics approaches. As far as data-based network inference methods are concerned, they enable the discovery of potential functional influences among molecular components. On the other hand, experimentally grounded network dynamical models have been shown to be perfectly suited for the mechanistic study of developmental processes. How do these two perspectives relate to each other? In this chapter, we describe and compare both approaches and then apply them to a given specific developmental module. Along with the step-by-step practical implementation of each approach, we also focus on discussing their respective goals, utility, assumptions, and associated limitations. We use the gene regulatory network (GRN) involved in Arabidopsis thaliana Root Stem Cell Niche patterning as our illustrative example. We show that descriptive models based on functional genomics data can provide important background information consistent with experimentally supported functional relationships integrated in mechanistic GRN models. The rationale of analysis and modeling can be applied to any other well-characterized functional developmental module in multicellular organisms, like plants and animals.

Mathematical models light up plant signaling

Plants respond to changes in the environment by triggering a suite of regulatory networks that control and synchronize molecular signaling in different tissues, organs, and the whole plant. Molecular studies through genetic and environmental perturbations, particularly in the model plant Arabidopsis thaliana, have revealed many of the mechanisms by which these responses are actuated. In recent years, mathematical modeling has become a complementary tool to the experimental approach that has furthered our understanding of biological mechanisms. In this review, we present modeling examples encompassing a range of different biological processes, in particular those regulated by light. Current issues and future directions in the modeling of plant systems are discussed.

Mechanical forces as information: an integrated approach to plant and animal development

Mechanical forces such as tension and compression act throughout growth and development of multicellular organisms. These forces not only affect the size and shape of the cells and tissues but are capable of modifying the expression of genes and the localization of molecular components within the cell, in the plasma membrane, and in the plant cell wall. The magnitude and direction of these physical forces change with cellular and tissue properties such as elasticity. Thus, mechanical forces and the mesoscopic fields that emerge from their local action constitute important sources of positional information. Moreover, physical and biochemical processes interact in non-linear ways during tissue and organ growth in plants and animals. In this review we discuss how such mechanical forces are generated, transmitted, and sensed in these two lineages of multicellular organisms to yield long-range positional information. In order to do so we first outline a potentially common basis for studying patterning and mechanosensing that relies on the structural principle of tensegrity, and discuss how tensegral structures might arise in plants and animals. We then provide some examples of morphogenesis in which mechanical forces appear to act as positional information during development, offering a possible explanation for ubiquitous processes, such as the formation of periodic structures. Such examples, we argue, can be interpreted in terms of tensegral phenomena. Finally, we discuss the hypothesis of mechanically isotropic points as a potentially generic mechanism for the localization and maintenance of stem-cell niches in multicellular organisms. This comparative approach aims to help uncovering generic mechanisms of morphogenesis and thus reach a better understanding of the evolution and development of multicellular phenotypes, focusing on the role of physical forces in these processes.

Proteomics in deciphering the auxin commitment in the Arabidopsis thaliana root growth

The development of plant root systems is characterized by a high plasticity, made possible by the continual propagation of new meristems. Root architecture is fundamental for overall plant growth, abiotic stress resistance, nutrient uptake, and response to environmental changes. Understanding the function of genes and proteins that control root architecture and stress resistance will contribute to the development of more sustainable systems of intensified crop production. To meet these challenges, proteomics provide the genome-wide scale characterization of protein expression pattern, subcellular localization, post-translational modifications, activity regulation, and molecular interactions. In this review, we describe a variety of proteomic strategies that have been applied to study the proteome of the whole organ and of specific cell types during root development. Each has advantages and limitations, but collectively they are providing important insights into the mechanisms by which auxin structures and patterns the root system and into the interplay between signaling networks, auxin transport and growth. The acquisition of proteomic, transcriptomic, and metabolomic data sets of the root apex on the cell scale has revealed the high spatial complexity of regulatory networks and fosters the use of new powerful proteomic tools for a full understanding of the control of root developmental processes and environmental responses.