BRAVO self-confined expression through WOX5 in the Arabidopsis root stem-cell niche.

In animals and plants, stem-cell niches are local microenvironments that are tightly regulated to preserve their unique identity while communicating with adjacent cells that will give rise to specialized cell types. In the primary root of Arabidopsis thaliana, two transcription factors, BRAVO and WOX5, among others, are expressed in the stem-cell niche. Intriguingly, BRAVO, a repressor of quiescent center divisions, confines its own gene expression to the stem-cell niche, as evidenced in a bravo mutant background. Here, we propose through mathematical modeling that BRAVO confines its own expression domain to the stem-cell niche by attenuating a WOX5-dependent diffusible activator of BRAVO. This negative feedback drives WOX5 activity to be spatially restricted as well. The results show that WOX5 diffusion and sequestration by binding to BRAVO are sufficient to drive the experimentally observed confined BRAVO expression at the stem-cell niche. We propose that the attenuation of a diffusible activator can be a general mechanism acting at other stem-cell niches to spatially confine genetic activity to a small region while maintaining signaling within them and with the surrounding cells.

Precise transcriptional control of cellular quiescence by BRAVO/WOX5 complex in Arabidopsis roots.

Understanding stem cell regulatory circuits is the next challenge in plant biology, as these cells are essential for tissue growth and organ regeneration in response to stress. In the Arabidopsis primary root apex, stem cell-specific transcription factors BRAVO and WOX5 co-localize in the quiescent centre (QC) cells, where they commonly repress cell division so that these cells can act as a reservoir to replenish surrounding stem cells, yet their molecular connection remains unknown. Genetic and biochemical analysis indicates that BRAVO and WOX5 form a transcription factor complex that modulates gene expression in the QC cells to preserve overall root growth and architecture. Furthermore, by using mathematical modelling we establish that BRAVO uses the WOX5/BRAVO complex to promote WOX5 activity in the stem cells. Our results unveil the importance of transcriptional regulatory circuits in plant stem cell development.

Landau theory for cellular patterns driven by lateral inhibition interaction.

The phenomenology of Landau theory with spatial coupling through diffusion has been widely used in the study of phase transitions and patterning. Here we follow this theory and apply it to study theoretically and numerically continuous and discontinuous transitions to periodic spatial cellular patterns driven by lateral inhibition coupling. As opposed to diffusion, lateral inhibition coupling drives differences between adjacent cells. We analyze the appearance of errors in these patterns (disordered metastable states) and propose mechanisms to prevent them. These mechanisms are based on a temporal-dependent lateral inhibition coupling strength, which can be mediated, among others, by gradients of diffusing molecules. The simplicity and generality of the framework used herein is expected to facilitate future analyses of additional phenomena taking place through lateral inhibition interactions in more complex scenarios.

Brassinosteroid signaling in plant development and adaptation to stress.

Brassinosteroids (BRs) are steroid hormones that are essential for plant growth and development. These hormones control the division, elongation and differentiation of various cell types throughout the entire plant life cycle. Our current understanding of the BR signaling pathway has mostly been obtained from studies using Arabidopsis thaliana as a model. In this context, the membrane steroid receptor BRI1 (BRASSINOSTEROID INSENSITIVE 1) binds directly to the BR ligand, triggering a signal cascade in the cytoplasm that leads to the transcription of BR-responsive genes that drive cellular growth. However, recent studies of the primary root have revealed distinct BR signaling pathways in different cell types and have highlighted cell-specific roles for BR signaling in controlling adaptation to stress. In this Review, we summarize our current knowledge of the spatiotemporal control of BR action in plant growth and development, focusing on BR functions in primary root development and growth, in stem cell self-renewal and death, and in plant adaption to environmental stress.

A Sizer model for cell differentiation in Arabidopsis thaliana root growth.

Plant roots grow due to cell division in the meristem and subsequent cell elongation and differentiation, a tightly coordinated process that ensures growth and adaptation to the changing environment. How the newly formed cells decide to stop elongating becoming fully differentiated is not yet understood. To address this question, we established a novel approach that combines the quantitative phenotypic variability of wild-type Arabidopsis roots with computational data from mathematical models. Our analyses reveal that primary root growth is consistent with a Sizer mechanism, in which cells sense their length and stop elongating when reaching a threshold value. The local expression of brassinosteroid receptors only in the meristem is sufficient to set this value. Analysis of roots insensitive to BR signaling and of roots with gibberellin biosynthesis inhibited suggests distinct roles of these hormones on cell expansion termination. Overall, our study underscores the value of using computational modeling together with quantitative data to understand root growth.

Redundancy and cooperation in Notch intercellular signaling.

During metazoan development, Notch signaling drives spatially coordinated differentiation by establishing communication between adjacent cells. This occurs through either lateral inhibition, in which adjacent cells acquire distinct fates, or lateral induction, in which all cells become equivalent. Notch signaling is commonly activated by several distinct ligands, each of which drives signaling with a different efficiency upon binding to the Notch receptor of adjacent cells. Moreover, these ligands can also be distinctly regulated by Notch signaling. Under such complex circumstances, the overall spatial coordination becomes elusive. Here, we address this issue through both mathematical and computational analyses. Our results show that when two ligands have distinct efficiencies and compete for the same Notch receptor, they cooperate to drive new signaling states, thereby conferring additional robustness and evolvability to Notch signaling. Counterintuitively, whereas antagonistically regulated ligands cooperate to drive and enhance the response that is expected from the more efficient ligand, equivalently regulated ligands coordinate emergent spatial responses that are dependent on both ligands. Our study highlights the importance of ligand efficiency in multi-ligand scenarios, and can explain previously reported complex phenotypes.

Experimental and Theoretical Methods to Approach the Study of Vascular Patterning in the Plant Shoot.

The plant vascular system provides transport and mechanical support functions that are essential for suitable plant growth and development. In Arabidopsis thaliana (Arabidopsis), the vascular tissues at the shoot inflorescence stems are disposed in organized vascular bundles. The vascular patterning emergence and development within the shoot inflorescence stems is under the control of plant growth regulators (De Rybel et al., Nat Rev Mol Cell Biol 17:30-40, 2016; Caño-Delgado et al., Annu Rev Cell Dev Biol 26:605-637, 2010). By using a combined approach of experimental methods for vascular tissues visualization and quantification together with theoretical methods through mathematical and computational modeling, we have reported that auxin transport and brassinosteroid signaling play complementary roles in the formation of the periodic vascular patterning in the shoot (Ibañes et al., Proc Natl Acad Sci U S A 106:13630-13635, 2009; Fàbregas et al., Plant Signal Behav 5:903-906, 2010; Fàbregas et al., PLoS Genet 11:e1005183, 2015). Here, we report the methodology for the interdisciplinary analysis of the shoot vascular patterning in the plant model Arabidopsis into a handle procedure for visualization, quantification, data analysis, and modeling implementation.

Methods for Modeling Brassinosteroid-Mediated Signaling in Plant Development.

Mathematical modeling of biological processes is a useful tool to draw conclusions that are contained in the data, but not directly reachable, as well as to make predictions and select the most efficient follow-up experiments. Here we outline a method to model systems of a few proteins that interact transcriptionally and/or posttranscriptionally, by representing the system as Ordinary Differential Equations and to study the model dynamics and stationary states. We exemplify this method by focusing on the regulation by the brassinosteroid (BR) signaling component BRASSINOSTEROID INSENSITIVE1 ETHYL METHYL SULFONATE SUPPRESSOR1 (BES1) of BRAVO, a quiescence-regulating transcription factor expressed in the quiescent cells of Arabidopsis thaliana roots. The method to extract the stationary states and the dynamics is provided as a Mathematica code and requires basic knowledge of the Mathematica software to be executed.

Single-cell telomere-length quantification couples telomere length to meristem activity and stem cell development in Arabidopsis.

Telomeres are specialized nucleoprotein caps that protect chromosome ends assuring cell division. Single-cell telomere quantification in animals established a critical role for telomerase in stem cells, yet, in plants, telomere-length quantification has been reported only at the organ level. Here, a quantitative analysis of telomere length of single cells in Arabidopsis root apex uncovered a heterogeneous telomere-length distribution of different cell lineages showing the longest telomeres at the stem cells. The defects in meristem and stem cell renewal observed in tert mutants demonstrate that telomere lengthening by TERT sets a replicative limit in the root meristem. Conversely, the long telomeres of the columella cells and the premature stem cell differentiation plt1,2 mutants suggest that differentiation can prevent telomere erosion. Overall, our results indicate that telomere dynamics are coupled to meristem activity and continuous growth, disclosing a critical association between telomere length, stem cell function, and the extended lifespan of plants.

Auxin influx carriers control vascular patterning and xylem differentiation in Arabidopsis thaliana.

Auxin is an essential hormone for plant growth and development. Auxin influx carriers AUX1/LAX transport auxin into the cell, while auxin efflux carriers PIN pump it out of the cell. It is well established that efflux carriers play an important role in the shoot vascular patterning, yet the contribution of influx carriers to the shoot vasculature remains unknown. Here, we combined theoretical and experimental approaches to decipher the role of auxin influx carriers in the patterning and differentiation of vascular tissues in the Arabidopsis inflorescence stem. Our theoretical analysis predicts that influx carriers facilitate periodic patterning and modulate the periodicity of auxin maxima. In agreement, we observed fewer and more spaced vascular bundles in quadruple mutants plants of the auxin influx carriers aux1lax1lax2lax3. Furthermore, we show AUX1/LAX carriers promote xylem differentiation in both the shoot and the root tissues. Influx carriers increase cytoplasmic auxin signaling, and thereby differentiation. In addition to this cytoplasmic role of auxin, our computational simulations propose a role for extracellular auxin as an inhibitor of xylem differentiation. Altogether, our study shows that auxin influx carriers AUX1/LAX regulate vascular patterning and differentiation in plants.

Pattern selection by dynamical biochemical signals.

The development of multicellular organisms involves cells to decide their fate upon the action of biochemical signals. This decision is often spatiotemporally coordinated such that a spatial pattern arises. The dynamics that drive pattern formation usually involve genetic nonlinear interactions and positive feedback loops. These complex dynamics may enable multiple stable patterns for the same conditions. Under these circumstances, pattern formation in a developing tissue involves a selection process: why is a certain pattern formed and not another stable one? Herein we computationally address this issue in the context of the Notch signaling pathway. We characterize a dynamical mechanism for developmental selection of a specific pattern through spatiotemporal changes of the control parameters of the dynamics, in contrast to commonly studied situations in which initial conditions and noise determine which pattern is selected among multiple stable ones. This mechanism can be understood as a path along the parameter space driven by a sequence of biochemical signals. We characterize the selection process for three different scenarios of this dynamical mechanism that can take place during development: the signal either 1) acts in all the cells at the same time, 2) acts only within a cluster of cells, or 3) propagates along the tissue. We found that key elements for pattern selection are the destabilization of the initial pattern, the subsequent exploration of other patterns determined by the spatiotemporal symmetry of the parameter changes, and the speeds of the path compared to the timescales of the pattern formation process itself. Each scenario enables the selection of different types of patterns and creates these elements in distinct ways, resulting in different features. Our approach extends the concept of selection involved in cellular decision-making, usually applied to cell-autonomous decisions, to systems that collectively make decisions through cell-to-cell interactions.

Regulation of plant stem cell quiescence by a brassinosteroid signaling module.

The quiescent center (QC) maintains the activity of the surrounding stem cells within the root stem cell niche, yet specific molecular players sustaining the low rate of QC cell division remain poorly understood. Here, we identified a R2R3-MYB transcription factor, BRAVO (BRASSINOSTEROIDS AT VASCULAR AND ORGANIZING CENTER), acting as a cell-specific repressor of QC divisions in the primary root of Arabidopsis. Ectopic BRAVO expression restricts overall root growth and ceases root regeneration upon damage of the stem cells, demonstrating the role of BRAVO in counteracting Brassinosteroid (BR)-mediated cell division in the QC cells. Interestingly, BR-regulated transcription factor BES1 (BRI1-EMS SUPRESSOR 1) directly represses and physically interacts with BRAVO in vivo, creating a switch that modulates QC divisions at the root stem cell niche. Together, our results define a mechanism for BR-mediated regulation of stem cell quiescence in plants.

Competition in notch signaling with cis enriches cell fate decisions.

Notch signaling is involved in cell fate choices during the embryonic development of Metazoa. Commonly, Notch signaling arises from the binding of the Notch receptor to its ligands in adjacent cells driving cell-to-cell communication. Yet, cell-autonomous control of Notch signaling through both ligand-dependent and ligand-independent mechanisms is known to occur as well. Examples include Notch signaling arising in the absence of ligand binding, and cis-inhibition of Notch signaling by titration of the Notch receptor upon binding to its ligands within a single cell. Increasing experimental evidences support that the binding of the Notch receptor with its ligands within a cell (cis-interactions) can also trigger a cell-autonomous Notch signal (cis-signaling), whose potential effects on cell fate decisions and patterning remain poorly understood. To address this question, herein we mathematically and computationally investigate the cell states arising from the combination of cis-signaling with additional Notch signaling sources, which are either cell-autonomous or involve cell-to-cell communication. Our study shows that cis-signaling can switch from driving cis-activation to effectively perform cis-inhibition and identifies under which conditions this switch occurs. This switch relies on the competition between Notch signaling sources, which share the same receptor but differ in their signaling efficiency. We propose that the role of cis-interactions and their signaling on fine-grained patterning and cell fate decisions is dependent on whether they drive cis-inhibition or cis-activation, which could be controlled during development. Specifically, cis-inhibition and not cis-activation facilitates patterning and enriches it by modulating the ratio of cells in the high-ligand expression state, by enabling additional periodic patterns like stripes and by allowing localized patterning highly sensitive to the precursor state and cell-autonomous bistability. Our study exemplifies the complexity of regulations when multiple signaling sources share the same receptor and provides the tools for their characterization.

Ligand-dependent Notch signaling strength orchestrates lateral induction and lateral inhibition in the developing inner ear.

During inner ear development, Notch exhibits two modes of operation: lateral induction, which is associated with prosensory specification, and lateral inhibition, which is involved in hair cell determination. These mechanisms depend respectively on two different ligands, jagged 1 (Jag1) and delta 1 (Dl1), that rely on a common signaling cascade initiated after Notch activation. In the chicken otocyst, expression of Jag1 and the Notch target Hey1 correlates well with lateral induction, whereas both Jag1 and Dl1 are expressed during lateral inhibition, as are Notch targets Hey1 and Hes5. Here, we show that Jag1 drives lower levels of Notch activity than Dl1, which results in the differential expression of Hey1 and Hes5. In addition, Jag1 interferes with the ability of Dl1 to elicit high levels of Notch activity. Modeling the sensory epithelium when the two ligands are expressed together shows that ligand regulation, differential signaling strength and ligand competition are crucial to allow the two modes of operation and for establishing the alternate pattern of hair cells and supporting cells. Jag1, while driving lateral induction on its own, facilitates patterning by lateral inhibition in the presence of Dl1. This novel behavior emerges from Jag1 acting as a competitive inhibitor of Dl1 for Notch signaling. Both modeling and experiments show that hair cell patterning is very robust. The model suggests that autoactivation of proneural factor Atoh1, upstream of Dl1, is a fundamental component for robustness. The results stress the importance of the levels of Notch signaling and ligand competition for Notch function.

Lateral inhibition and neurogenesis: novel aspects in motion.

Neuronal production in metazoans is tightly controlled by Delta/Notch-dependent signals regulating lateral inhibition. It is currently thought that lateral inhibition takes place in clusters of precursors with equal capacity to trigger and receive Notch-dependent inhibitory signals. However, this view neglects crucial dynamical aspects of the process. In this review, we discuss two of these dynamic factors, whose alterations yield dysfunctions in neurogenesis. First, precursors show variable neurogenic capacity as they go through the cell cycle. Second, differentiating precursors are in direct contact with non-neurogenic cells at the wavefront of expanding neurogenic domains. We discuss the mechanisms adopted by Metazoa to prevent these dysfunctions in the lateral inhibitory process, which include cell cycle synchronization occurring in the invertebrate neural epithelium and during primary neurogenesis in anamniotes, interkinetic nuclear movement in the vertebrate neuroepithelium and generalized Delta expression ahead of the neurogenic wavefront. The emerging concept is that lateral inhibition during neurogenesis occurs in dynamic clusters of precursors and requires specific mechanisms to avoid distortions resulting from the interaction between neurogenic and non-neurogenic precursors. The advance in visualizing Notch dynamics with real-time imaging at cellular and subcellular levels will notably contribute to our understanding of these novel "aspects of motion" in neurogenesis.

Regulation of neuronal differentiation at the neurogenic wavefront.

Signaling mediated by the Delta/Notch system controls the process of lateral inhibition, known to regulate neurogenesis in metazoans. Lateral inhibition takes place in equivalence groups formed by cells having equal capacity to differentiate, and it results in the singling out of precursors, which subsequently become neurons. During normal development, areas of active neurogenesis spread through non-neurogenic regions in response to specific morphogens, giving rise to neurogenic wavefronts. Close contact of these wavefronts with non-neurogenic cells is expected to affect lateral inhibition. Therefore, a mechanism should exist in these regions to prevent disturbances of the lateral inhibitory process. Focusing on the developing chick retina, we show that Dll1 is widely expressed by non-neurogenic precursors located at the periphery of this tissue, a region lacking Notch1, lFng, and differentiation-related gene expression. We investigated the role of this Dll1 expression through mathematical modeling. Our analysis predicts that the absence of Dll1 ahead of the neurogenic wavefront results in reduced robustness of the lateral inhibition process, often linked to enhanced neurogenesis and the presence of morphological alterations of the wavefront itself. These predictions are consistent with previous observations in the retina of mice in which Dll1 is conditionally mutated. The predictive capacity of our mathematical model was confirmed further by mimicking published results on the perturbation of morphogenetic furrow progression in the eye imaginal disc of Drosophila. Altogether, we propose that Notch-independent Delta expression ahead of the neurogenic wavefront is required to avoid perturbations in lateral inhibition and wavefront progression, thus optimizing the neurogenic process.

Asymmetric stochastic switching driven by intrinsic molecular noise.

Low-copy-number molecules are involved in many functions in cells. The intrinsic fluctuations of these numbers can enable stochastic switching between multiple steady states, inducing phenotypic variability. Herein we present a theoretical and computational study based on Master Equations and Fokker-Planck and Langevin descriptions of stochastic switching for a genetic circuit of autoactivation. We show that in this circuit the intrinsic fluctuations arising from low-copy numbers, which are inherently state-dependent, drive asymmetric switching. These theoretical results are consistent with experimental data that have been reported for the bistable system of the gallactose signaling network in yeast. Our study unravels that intrinsic fluctuations, while not required to describe bistability, are fundamental to understand stochastic switching and the dynamical relative stability of multiple states.

A systems biology approach to dissect the contribution of brassinosteroid and auxin hormones to vascular patterning in the shoot of Arabidopsis thaliana.

Systems biology can foster our understanding of hormonal regulation of plant vasculature. One such example is our recent study on the role of plant hormones brassinosteroid (BR) and auxin in vascular patterning of Arabidopsis thaliana (Arabidopsis) shoots. By using a combined approach of mathematical modelling and molecular genetics, we have reported that auxin and BRs have complementary effects in the formation of the shoot vascular pattern. We proposed that auxin maxima, driven by auxin polar transport, position vascular bundles in the stem. BRs in turn modulate the number of vascular bundles, potentially by controlling cell division dynamics that enhance the number of provascular cells. Future interdisciplinary studies connecting vascular initiation at the shoot apex with the established vascular pattern in the basal part of the plant stem are now required to understand how and when the shoot vascular pattern emerges in the plant.

Brassinosteroid signaling and auxin transport are required to establish the periodic pattern of Arabidopsis shoot vascular bundles.

The plant vascular system provides transport and support capabilities that are essential for plant growth and development, yet the mechanisms directing the arrangement of vascular bundles within the shoot inflorescence stem remain unknown. We used computational and experimental biology to evaluate the role of auxin and brassinosteroid hormones in vascular patterning in Arabidopsis. We show that periodic auxin maxima controlled by polar transport and not overall auxin levels underlie vascular bundle spacing, whereas brassinosteroids modulate bundle number by promoting early procambial divisions. Overall, this study demonstrates that auxin polar transport coupled to brassinosteroid signaling is required to determine the radial pattern of vascular bundles in shoots.

Left-right axis determination.

Vertebrates display left-right (L-R) asymmetric organ positioning and morphologies, which are established during embryonic development. These asymmetries are conserved among individuals and species. How, when and where do embryos first break the symmetry? Why is it broken in a consistent direction? How is the asymmetry transmitted to and coordinated within the whole embryo? Which of these elements are conserved between different organisms? These questions have been the focus of intense research during the last decade, and much has been learned. Nonetheless, our understanding of how tissue and organ L-R differences are established during embryogenesis is scarce. A systems biology approach may enable us to better understand the dynamics of gene networks, epigenetics, cilia, fluids, and charged molecules as well as other processes involved in the generation of the vertebrate L-R axis.