Self-organized pattern formation in the developing mouse neural tube by a temporal relay of BMP signaling

Developing tissues interpret dynamic changes in morphogen activity to generate cell type diversity. To quantitatively study bone morphogenetic protein (BMP) signaling dynamics in the mouse neural tube, we developed an embryonic stem cell differentiation system tailored for growing tissues. Differentiating cells form striking self-organized patterns of dorsal neural tube cell types driven by sequential phases of BMP signaling that are observed both in vitro and in vivo. Data-driven biophysical modeling showed that these dynamics result from coupling fast negative feedback with slow positive regulation of signaling by the specification of an endogenous BMP source. Thus, in contrast to relays that propagate morphogen signaling in space, we identify a BMP signaling relay that operates in time. This mechanism allows for a rapid initial concentration-sensitive response that is robustly terminated, thereby regulating balanced sequential cell type generation. Our study provides an experimental and theoretical framework to understand how signaling dynamics are exploited in developing tissues.

Decaying and expanding Erk gradients process memory of skeletal size during zebrafish fin regeneration

Regeneration of an amputated salamander limb or fish fin restores pre-injury size and structure, illustrating the phenomenon of positional memory. Although appreciated for centuries, the identity of position-dependent cues and how they control tissue growth are not resolved. Here, we quantify Erk signaling events in whole populations of osteoblasts during zebrafish fin regeneration. We find that osteoblast Erk activity is dependent on Fgf receptor signaling and organized into millimeter-long gradients that extend from the distal tip to the amputation site. Erk activity scales with the amount of tissue amputated, predicts the likelihood of osteoblast cycling, and predicts the size of regenerated skeletal structures. Mathematical modeling suggests gradients are established by the transient deposition of long-lived ligands that are transported by tissue growth. This concept is supported by the observed scaling of expression of the essential epidermal ligand fgf20a with extents of amputation. Our work provides evidence that localized, scaled expression of pro-regenerative ligands instructs long-range signaling and cycling to control skeletal size in regenerating appendages.

Dissecting the mystery of embryonic scaling: The Scalers Hypothesis and its confirmation in sea urchin embryos

Embryonic scaling, the ability of embryos to regulate their spatial structure in proportion to size, remains a fascinating yet poorly studied problem in developmental biology. First described in sea urchin embryos by Hans Driesch, this phenomenon is now recognized as a striking example of how living organisms use non-equilibrium self-organization, based on reaction-diffusion (RD) systems, to generate pattern-determining morphogen concentration gradients that scale with size. Although specific molecular mechanisms for scaling such gradients have been described in some cases, a general approach for the targeted identification of such mechanisms had not been developed until recently. In search of a solution, we hypothesized the obligatory participation in scaling mechanisms of special genes, which we named "scalers." We supposed that these genes share two critical features: their expression is sensitive to embryo size, and their protein products determine the scale of morphogen concentration gradients. As proof of principle, we recently identified scalers by detecting differentially expressed genes in wild-type and half-size Xenopus laevis gastrula embryos. Furthermore, we described a mechanism by which one of the identified scalers, the gene encoding Metalloproteinase 3 (Mmp3), regulates the scaling of gradients of the morphogenic protein Bmp and its antagonists, Chordin and Noggin1/2. In the present work, we have made an important theoretical generalization of the Scalers Hypothesis by proving a statement regarding the obligatory presence of scalers in closed RD systems generating morphogen concentration gradients. Furthermore, through a systematic analysis of all known types of embryonic scaling models based on RD systems, we demonstrate that scalers are present in all known types of such models, either explicitly or implicitly. Finally, to test the universality of the Scalers Hypothesis, we applied our method to identify scalers that adjust Bmp/Chordin gradients to the size of the sea urchin embryo, Strongylocentrotus droebachiensis. Our results show that at least two members of the gene cluster encoding astacin metalloproteinases of the Span family, namely bp10 and Span, exhibit properties characteristic of scalers. Namely, their expression levels increase significantly in half-size embryos, and their protein products specifically degrade Chordin. Additionally, we found that the loss of function of bp10 and span leads to a narrowing of the dorsal domain of the Bmp signaling nuclear effector, pSmad1/5. These findings not only validate the Scalers Hypothesis but also uncover a novel mechanism by which Span proteinases fine-tune Chordin and Bmp morphogen concentration gradients in sea urchins. Thus, the Scalers Hypothesis and the approach to targeted search for such genes developed on its basis open up promising avenues for future research into scaling mechanisms in various biological systems.

Dynamics of morphogen source formation in a growing tissue

A tight regulation of morphogen production is key for morphogen gradient formation and thereby for reproducible and organised organ development. Although many genetic interactions involved in the establishment of morphogen production domains are known, the biophysical mechanisms of morphogen source formation are poorly understood. Here we addressed this by focusing on the morphogen Sonic hedgehog (Shh) in the vertebrate neural tube. Shh is produced by the adjacently located notochord and by the floor plate of the neural tube. Using a data-constrained computational screen, we identified different possible mechanisms by which floor plate formation can occur, only one of which is consistent with experimental data. In this mechanism, the floor plate is established rapidly in response to Shh from the notochord and the dynamics of regulatory interactions within the neural tube. In this process, uniform activators and Shh-dependent repressors are key for establishing the floor plate size. Subsequently, the floor plate becomes insensitive to Shh and increases in size due to tissue growth, leading to scaling of the floor plate with neural tube size. In turn, this results in scaling of the Shh amplitude with tissue growth. Thus, this mechanism ensures a separation of time scales in floor plate formation, so that the floor plate domain becomes growth-dependent after an initial rapid establishment phase. Our study raises the possibility that the time scale separation between specification and growth might be a common strategy for scaling the morphogen gradient amplitude in growing organs. The model that we developed provides a new opportunity for quantitative studies of morphogen source formation in growing tissues.

Morphogens in the evolution of size, shape and patterning

Much of the striking diversity of life on Earth has arisen from variations in the way that the same molecules and networks operate during development to shape and pattern tissues and organs into different morphologies. However, we still understand very little about the potential for diversification exhibited by different, highly conserved mechanisms during evolution, or, conversely, the constraints that they place on evolution. With the aim of steering the field in new directions, we focus on morphogen-mediated patterning and growth as a case study to demonstrate how conserved developmental mechanisms can adapt during evolution to drive morphological diversification and optimise functionality, and to illustrate how evolution algorithms and computational tools can be used alongside experiments to provide insights into how these conserved mechanisms can evolve. We first introduce key conserved properties of morphogen-driven patterning mechanisms, before summarising comparative studies that exemplify how changes in the spatiotemporal expression and signalling levels of morphogens impact the diversification of organ size, shape and patterning in nature. Finally, we detail how theoretical frameworks can be used in conjunction with experiments to probe the role of morphogen-driven patterning mechanisms in evolution. We conclude that morphogen-mediated patterning is an excellent model system and offers a generally applicable framework to investigate the evolution of developmental mechanisms.

'Three signals - three body axes' as patterning principle in bilaterians

In vertebrates, the three orthogonal body axes, anteroposterior (AP), dorsoventral (DV) and left-right (LR) are determined at gastrula and neurula stages by the Spemann-Mangold organizer and its equivalents. A common feature of AP and DV axis formation is that an evolutionary conserved interplay between growth factors (Wnt, BMP) and their extracellular antagonists (e.g. Dkk1, Chordin) creates signaling gradients for axial patterning. Recent work showed that LR patterning in Xenopus follows the same principle, with R-spondin 2 (Rspo2) as an extracellular FGF antagonist, which creates a signaling gradient that determines the LR vector. That a triad of anti-FGF, anti-BMP, and anti-Wnt governs LR, DV, and AP axis formation reveals a unifying principle in animal development. We discuss how cross-talk between these three signals confers integrated AP-DV-LR body axis patterning underlying developmental robustness, size scaling, and harmonious regulation. We propose that Urbilateria featured three orthogonal body axes that were governed by a Cartesian coordinate system of orthogonal Wnt/AP, BMP/DV, and FGF/LR signaling gradients.

How a reaction-diffusion signal can control spinal cord regeneration in axolotls: A modeling study

Axolotls are uniquely able to completely regenerate the spinal cord after amputation. The underlying governing mechanisms of this regenerative response have not yet been fully elucidated. We previously found that spinal cord regeneration is mainly driven by cell-cycle acceleration of ependymal cells, recruited by a hypothetical signal propagating from the injury. However, the nature of the signal and its propagation remain unknown. In this theoretical study, we investigated whether the regeneration-inducing signal can follow a reaction-diffusion process. We developed a computational model, validated it with experimental data, and showed that the signal dynamics can be understood in terms of reaction-diffusion mechanism. By developing a theory of the regenerating outgrowth in the limit of fast reaction-diffusion, we demonstrate that control of regenerative response solely relies on cell-to-signal sensitivity and the signal reaction-diffusion characteristic length. This study lays foundations for further identification of the signal controlling regeneration of the spinal cord.

An emerging role for tissue plasticity in developmental precision

Reproducible tissue morphology is a fundamental feature of embryonic development. To ensure such robustness during tissue morphogenesis, inherent noise in biological processes must be buffered. While redundant genes, parallel signaling pathways and intricate network topologies are known to reduce noise, over the last few years, mechanical properties of tissues have been shown to play a vital role. Here, taking the example of somite shape changes, I will discuss how tissues are highly plastic in their ability to change shapes leading to increased precision and reproducibility.

Scaling between cell cycle duration and wing growth is regulated by Fat-Dachsous signaling in Drosophila

The atypical cadherins Fat and Dachsous (Ds) signal through the Hippo pathway to regulate growth of numerous organs, including the Drosophila wing. Here, we find that Ds-Fat signaling tunes a unique feature of cell proliferation found to control the rate of wing growth during the third instar larval phase. The duration of the cell cycle increases in direct proportion to the size of the wing, leading to linear-like growth during the third instar. Ds-Fat signaling enhances the rate at which the cell cycle lengthens with wing size, thus diminishing the rate of wing growth. We show that this results in a complex but stereotyped relative scaling of wing growth with body growth in Drosophila. Finally, we examine the dynamics of Fat and Ds protein distribution in the wing, observing graded distributions that change during growth. However, the significance of these dynamics is unclear since perturbations in expression have negligible impact on wing growth.

Contact area and tissue growth dynamics shape synthetic juxtacrine signaling patterns

Cell-cell communication through direct contact, or juxtacrine signaling, is important in development, disease, and many areas of physiology. Synthetic forms of juxtacrine signaling can be precisely controlled and operate orthogonally to native processes, making them a powerful reductionist tool with which to address fundamental questions in cell-cell communication in vivo. Here we investigate how cell-cell contact length and tissue growth dynamics affect juxtacrine signal responses through implementing a custom synthetic gene circuit in Drosophila wing imaginal discs alongside mathematical modeling to determine synthetic Notch (synNotch) activation patterns. We find that the area of contact between cells largely determines the extent of synNotch activation, leading to the prediction that the shape of the interface between signal-sending and signal-receiving cells will impact the magnitude of the synNotch response. Notably, synNotch outputs form a graded spatial profile that extends several cell diameters from the signal source, providing evidence that the response to juxtacrine signals can persist in cells as they proliferate away from source cells, or that cells remain able to communicate directly over several cell diameters. Our model suggests the former mechanism may be sufficient, since it predicts graded outputs without diffusion or long-range cell-cell communication. Overall, we identify that cell-cell contact area together with output synthesis and decay rates likely govern the pattern of synNotch outputs in both space and time during tissue growth, insights that may have broader implications for juxtacrine signaling in general.

Scaling between cell cycle duration and wing growth is regulated by Fat-Dachsous signaling in Drosophila

The atypical cadherins Fat and Dachsous (Ds) signal through the Hippo pathway to regulate growth of numerous organs, including the Drosophila wing. Here, we find that Ds-Fat signaling tunes a unique feature of cell proliferation found to control the rate of wing growth during the third instar larval phase. The duration of the cell cycle increases in direct proportion to the size of the wing, leading to linear-like growth during the third instar. Ds-Fat signaling enhances the rate at which the cell cycle lengthens with wing size, thus diminishing the rate of wing growth. We show that this results in a complex but stereotyped relative scaling of wing growth with body growth in Drosophila. Finally, we examine the dynamics of Fat and Ds protein distribution in the wing, observing graded distributions that change during growth. However, the significance of these dynamics is unclear since perturbations in expression have negligible impact on wing growth.

Balancing competing effects of tissue growth and cytoskeletal regulation during Drosophila wing disc development

How a developing organ robustly coordinates the cellular mechanics and growth to reach a final size and shape remains poorly understood. Through iterations between experiments and model simulations that include a mechanistic description of interkinetic nuclear migration, we show that the local curvature, height, and nuclear positioning of cells in the Drosophila wing imaginal disc are defined by the concurrent patterning of actomyosin contractility, cell-ECM adhesion, ECM stiffness, and interfacial membrane tension. We show that increasing cell proliferation via different growth-promoting pathways results in two distinct phenotypes. Triggering proliferation through insulin signaling increases basal curvature, but an increase in growth through Dpp signaling and Myc causes tissue flattening. These distinct phenotypic outcomes arise from differences in how each growth pathway regulates the cellular cytoskeleton, including contractility and cell-ECM adhesion. The coupled regulation of proliferation and cytoskeletal regulators is a general strategy to meet the multiple context-dependent criteria defining tissue morphogenesis.

Bone morphogenetic protein signaling: the pathway and its regulation

In the mid-1960s, bone morphogenetic proteins (BMPs) were first identified in the extracts of bone to have the remarkable ability to induce heterotopic bone. When the Drosophila gene decapentaplegic (dpp) was first identified to share sequence similarity with mammalian BMP2/BMP4 in the late-1980s, it became clear that secreted BMP ligands can mediate processes other than bone formation. Following this discovery, collaborative efforts between Drosophila geneticists and mammalian biochemists made use of the strengths of their respective model systems to identify BMP signaling components and delineate the pathway. The ability to conduct genetic modifier screens in Drosophila with relative ease was critical in identifying the intracellular signal transducers for BMP signaling and the related transforming growth factor-beta/activin signaling pathway. Such screens also revealed a host of genes that encode other core signaling components and regulators of the pathway. In this review, we provide a historical account of this exciting time of gene discovery and discuss how the field has advanced over the past 30 years. We have learned that while the core BMP pathway is quite simple, composed of 3 components (ligand, receptor, and signal transducer), behind the versatility of this pathway lies multiple layers of regulation that ensures precise tissue-specific signaling output. We provide a sampling of these discoveries and highlight many questions that remain to be answered to fully understand the complexity of BMP signaling.

Dally is not essential for Dpp spreading or internalization but for Dpp stability by antagonizing Tkv-mediated Dpp internalization

Dpp/BMP acts as a morphogen to provide positional information in the Drosophila wing disc. Key cell-surface molecules to control Dpp morphogen gradient formation and signaling are heparan sulfate proteoglycans (HSPGs). In the wing disc, two HSPGs, the glypicans Division abnormally delayed (Dally) and Dally-like (Dlp) have been suggested to act redundantly to control these processes through direct interaction of their heparan sulfate (HS) chains with Dpp. Based on this assumption, a number of models on how glypicans control Dpp gradient formation and signaling have been proposed, including facilitating or hindering Dpp spreading, stabilizing Dpp on the cell surface, or recycling Dpp. However, how distinct HSPGs act remains largely unknown. Here, we generate genome-engineering platforms for the two glypicans and find that only Dally is critical for Dpp gradient formation and signaling through interaction of its core protein with Dpp. We also find that this interaction is not sufficient and that the HS chains of Dally are essential for these functions largely without interacting with Dpp. We provide evidence that the HS chains of Dally are not essential for spreading or recycling of Dpp but for stabilizing Dpp on the cell surface by antagonizing receptor-mediated Dpp internalization. These results provide new insights into how distinct HSPGs control morphogen gradient formation and signaling during development.

Patterned apoptosis has an instructive role for local growth and tissue shape regulation in a fast-growing epithelium

What regulates organ size and shape remains one fundamental mystery of modern biology. Research in this area has primarily focused on deciphering the regulation in time and space of growth and cell division, while the contribution of cell death has been overall neglected. This includes studies of the Drosophila wing, one of the best-characterized systems for the study of growth and patterning, undergoing massive growth during larval stage and important morphogenetic remodeling during pupal stage. So far, it has been assumed that cell death was relatively neglectable in this tissue both during larval stage and pupal stage, and as a result, the pattern of growth was usually attributed to the distribution of cell division. Here, using systematic mapping and registration combined with quantitative assessment of clone size and disappearance as well as live imaging, we outline a persistent pattern of cell death and clone elimination emerging in the larval wing disc and persisting during pupal wing morphogenesis. Local variation of cell death is associated with local variation of clone size, pointing to an impact of cell death on local growth that is not fully compensated by proliferation. Using morphometric analyses of adult wing shape and genetic perturbations, we provide evidence that patterned death locally and globally affects adult wing shape and size. This study describes a roadmap for precise assessment of the contribution of cell death to tissue shape and outlines an important instructive role of cell death in modulating quantitatively local growth and morphogenesis of a fast-growing tissue.

Quantitative Live Imaging of Zebrafish Scale Regeneration: From Adult Fish to Signaling Patterns and Tissue Flows

In regeneration, a damaged body part grows back to its original form. Understanding the mechanisms and physical principles underlying this process has been limited by the difficulties of visualizing cell signals and behaviors in regeneration. Zebrafish scales are emerging as a model system to investigate morphogenesis during vertebrate regeneration using quantitative live imaging. Scales are millimeter-sized dermal bone disks forming a skeletal armor on the body of the fish. The scale bone is deposited by an adjacent monolayer of osteoblasts that, after scale loss, regenerates in about 2 weeks. This intriguing regenerative process is accessible to live confocal microscopy, quantifications, and mathematical modeling. Here, I describe methods to image scale regeneration live, tissue-wide and at sub-cellular resolution. Furthermore, I describe methods to process the resulting images and quantify cell, tissue, and signal dynamics.

Genome-wide analysis of BMP/GDF family and DAP-seq of YY1 suggest their roles in Cynoglossus semilaevis sexual size dimorphism

Sexual size dimorphism (SSD) characterized by different body size between females and males have been reported in various animals. Gonadectomy experiments have implied important regulatory roles of the gonad in SSD. Among multiple factors from the gonad, TGF-β superfamily (especially BMP/GDF family) attracted our interest due to its pleiotropy in growth and reproduction regulations. Thus, whether BMP/GDF family members serve as crucial regulators for SSD was studied in a typically female-biased SSD flatfish named Chinese tongue sole (Cynoglossus semilaevis). Firstly, a total of 26 BMP/GDF family members were identified. The PPI network analysis showed that they may interact with ACVR2a, ACVR2b, ACVR1, BMPR2, SMAD3, BMPR1a, and other proteins. Subsequently, DAP-seq was employed to reveal the binding sites for yin yang 1 (yy1), a transcription factor involved in gonad function and cell growth partly by regulating TGF-β superfamily. The results revealed that two yy1 homologues yy1a and yy1b in C. semilaevis could regulate Hippo signaling pathway, mTOR signaling pathway, and AMPK signaling pathway. Moreover, BMP/GDF family genes including bmp2, bmp4, bmp5, gdf6a, and gdf6b were important components of Hippo pathway. In future, the crosstalk among yy1a, yy1b, and TGF-β family would provide more insight into sexual size dimorphism in C. semilaevis.

Geometric effects position renal vesicles during kidney development

During kidney development, reciprocal signaling between the epithelium and the mesenchyme coordinates nephrogenesis with branching morphogenesis of the collecting ducts. The mechanism that positions the renal vesicles, and thus the nephrons, relative to the branching ureteric buds has remained elusive. By combining computational modeling and experiments, we show that geometric effects concentrate the key regulator, WNT9b, at the junctions between parent and daughter branches where renal vesicles emerge, even when uniformly expressed in the ureteric epithelium. This curvature effect might be a general paradigm to create non-uniform signaling in development.

Effect of substrate heterogeneity and topology on epithelial tissue growth dynamics

Tissue growth kinetics and interface dynamics depend on the properties of the tissue environment and cell-cell interactions. In cellular environments, substrate heterogeneity and geometry arise from a variety factors, such as the structure of the extracellular matrix and nutrient concentration. We used the CellSim3D model, a kinetic cell division simulator, to investigate the growth kinetics and interface roughness dynamics of epithelial tissue growth on heterogeneous substrates with varying topologies. The results show that the presence of quenched disorder has a clear effect on the colony morphology and the roughness scaling of the interface in the moving interface regime. In a medium with quenched disorder, the tissue interface has a smaller interface roughness exponent, α, and a larger growth exponent, β. The scaling exponents also depend on the topology of the substrate and cannot be categorized by well-known universality classes.

2D effects enhance precision of gradient-based tissue patterning

Robust embryonic development requires pattern formation with high spatial accuracy. In epithelial tissues that are patterned by morphogen gradients, the emerging patterns achieve levels of precision that have recently been explained by a simple one-dimensional reaction-diffusion model with kinetic noise. Here, we show that patterning precision is even greater if transverse diffusion effects are at play in such tissues. The positional error, a measure for spatial patterning accuracy, decreases in wider tissues but then saturates beyond a width of about ten cells. This demonstrates that the precision of gradient-based patterning in two- or higher-dimensional systems can be even greater than predicted by 1D models, and further attests to the potential of noisy morphogen gradients for high-precision tissue patterning.

The Unreasonable Effectiveness of Reaction Diffusion in Vertebrate Skin Color Patterning

In 1952, Alan Turing published the reaction-diffusion (RD) mathematical framework, laying the foundations of morphogenesis as a self-organized process emerging from physicochemical first principles. Regrettably, this approach has been widely doubted in the field of developmental biology. First, we summarize Turing's line of thoughts to alleviate the misconception that RD is an artificial mathematical construct. Second, we discuss why phenomenological RD models are particularly effective for understanding skin color patterning at the meso/macroscopic scales, without the need to parameterize the profusion of variables at lower scales. More specifically, we discuss how RD models (a) recapitulate the diversity of actual skin patterns, (b) capture the underlying dynamics of cellular interactions, (c) interact with tissue size and shape, (d) can lead to ordered sequential patterning, (e) generate cellular automaton dynamics in lizards and snakes, (f) predict actual patterns beyond their statistical features, and (g) are robust to model variations. Third, we discuss the utility of linear stability analysis and perform numerical simulations to demonstrate how deterministic RD emerges from the underlying chaotic microscopic agents.

Is Drosophila Dpp/BMP morphogen spreading required for wing patterning and growth?

Secreted signaling molecules act as morphogens to control patterning and growth in many developing tissues. Since locally produced morphogens spread to form a concentration gradient in the surrounding tissue, spreading is generally thought to be the key step in the non-autonomous actions. Here, we review recent advances in tool development to investigate morphogen function using the role of decapentaplegic (Dpp)/bone morphogenetic protein (BMP)-type ligand in the Drosophila wing disc as an example. By applying protein binder tools to distinguish between the roles of Dpp spreading and local Dpp signaling, we found that Dpp signaling in the source cells is important for wing patterning and growth but Dpp spreading from this source cells is not as strictly required as previously thought. Given recent studies showing unexpected requirements of long-range action of different morphogens, manipulating endogenous morphogen gradients by synthetic protein binder tools could shed more light on how morphogens act in developing tissues.

Somitic positional information guides self-organized patterning of snake scales

Two influential concepts in tissue patterning are Wolpert's positional information and Turing's self-organized reaction-diffusion (RD). The latter establishes the patterning of hair and feathers. Here, our morphological, genetic, and functional-by CRISPR-Cas9-mediated gene disruption-characterization of wild-type versus "scaleless" snakes reveals that the near-perfect hexagonal pattern of snake scales is established through interactions between RD in the skin and somitic positional information. First, we show that ventral scale development is guided by hypaxial somites and, second, that ventral scales and epaxial somites guide the sequential RD patterning of the dorsolateral scales. The RD intrinsic length scale evolved to match somite periodicity, ensuring the alignment of ribs and scales, both of which play a critical role in snake locomotion.

A multiscale chemical-mechanical model predicts impact of morphogen spreading on tissue growth

The exact mechanism controlling cell growth remains a grand challenge in developmental biology and regenerative medicine. The Drosophila wing disc tissue serves as an ideal biological model to study mechanisms involved in growth regulation. Most existing computational models for studying tissue growth focus specifically on either chemical signals or mechanical forces. Here we developed a multiscale chemical-mechanical model to investigate the growth regulation mechanism based on the dynamics of a morphogen gradient. By comparing the spatial distribution of dividing cells and the overall tissue shape obtained in model simulations with experimental data of the wing disc, it is shown that the size of the domain of the Dpp morphogen is critical in determining tissue size and shape. A larger tissue size with a faster growth rate and more symmetric shape can be achieved if the Dpp gradient spreads in a larger domain. Together with Dpp absorbance at the peripheral zone, the feedback regulation that downregulates Dpp receptors on the cell membrane allows for further spreading of the morphogen away from its source region, resulting in prolonged tissue growth at a more spatially homogeneous growth rate.

The impact of cell size on morphogen gradient precision

Tissue patterning during embryonic development is remarkably precise. Here, we numerically determine the impact of the cell diameter, gradient length and the morphogen source on the variability of morphogen gradients. We show that the positional error increases with the gradient length relative to the size of the morphogen source, and with the square root of the cell diameter and the readout position. We provide theoretical explanations for these relationships, and show that they enable high patterning precision over developmental time for readouts that scale with expanding tissue domains, as observed in the Drosophila wing disc. Our analysis suggests that epithelial tissues generally achieve higher patterning precision with small cross-sectional cell areas. An extensive survey of measured apical cell areas shows that they are indeed small in developing tissues that are patterned by morphogen gradients. Enhanced precision may thus have led to the emergence of pseudostratification in epithelia, a phenomenon for which the evolutionary benefit had so far remained elusive.

Patterning precision under non-linear morphogen decay and molecular noise

Morphogen gradients can instruct cells about their position in a patterned tissue. Non-linear morphogen decay has been suggested to increase gradient precision by reducing the sensitivity to variability in the morphogen source. Here, we use cell-based simulations to quantitatively compare the positional error of gradients for linear and non-linear morphogen decay. While we confirm that non-linear decay reduces the positional error close to the source, the reduction is very small for physiological noise levels. Far from the source, the positional error is much larger for non-linear decay in tissues that pose a flux barrier to the morphogen at the boundary. In light of this new data, a physiological role of morphogen decay dynamics in patterning precision appears unlikely.

Cell cycle dynamics control fluidity of the developing mouse neuroepithelium

As developing tissues grow in size and undergo morphogenetic changes, their material properties may be altered. Such changes result from tension dynamics at cell contacts or cellular jamming. Yet, in many cases, the cellular mechanisms controlling the physical state of growing tissues are unclear. We found that at early developmental stages, the epithelium in the developing mouse spinal cord maintains both high junctional tension and high fluidity. This is achieved via a mechanism in which interkinetic nuclear movements generate cell area dynamics that drive extensive cell rearrangements. Over time, the cell proliferation rate declines, effectively solidifying the tissue. Thus, unlike well-studied jamming transitions, the solidification uncovered here resembles a glass transition that depends on the dynamical stresses generated by proliferation and differentiation. Our finding that the fluidity of developing epithelia is linked to interkinetic nuclear movements and the dynamics of growth is likely to be relevant to multiple developing tissues.

Coordinated growth of linked epithelia is mediated by the Hippo pathway

An epithelium in a living organism seldom develops in isolation. Rather, most epithelia are tethered to other epithelial or non-epithelial tissues, necessitating growth coordination between layers. We investigated how two tethered epithelial layers of the Drosophila larval wing imaginal disc, the disc proper (DP) and the peripodial epithelium (PE), coordinate their growth. DP growth is driven by the morphogens Hedgehog (Hh) and Dpp, but regulation of PE growth is poorly understood. We find that the PE adapts to changes in growth rates of the DP, but not vice versa, suggesting a "leader and follower" mechanism. Moreover, PE growth can occur by cell shape changes, even when proliferation is inhibited. While Hh and Dpp pattern gene expression in both layers, growth of the DP is exquisitely sensitive to Dpp levels, while growth of the PE is not; the PE can achieve an appropriate size even when Dpp signaling is inhibited. Instead, both the growth of the PE and its accompanying cell shape changes require the activity of two components of the mechanosensitive Hippo pathway, the DNA-binding protein Scalloped (Sd) and its co-activator (Yki), which could allow the PE to sense and respond to forces generated by DP growth. Thus, an increased reliance on mechanically-dependent growth mediated by the Hippo pathway, at the expense of morphogen-dependent growth, enables the PE to evade layer-intrinsic growth control mechanisms and coordinate its growth with the DP. This provides a potential paradigm for growth coordination between different components of a developing organ.

Stemming Tumoral Growth: A Matter of Grotesque Organogenesis

The earliest metazoans probably evolved from single-celled organisms which found the colonial system to be a beneficial organization. Over the course of their evolution, these primary colonial organisms increased in size, and division of labour among the cells became a remarkable feature, leading to a higher level of organization: the biological organs. Primitive metazoans were the first organisms in evolution to show organ-type structures, which set the grounds for complex organs to evolve. Throughout evolution, and concomitant with organogenesis, is the appearance of tissue-specific stem cells. Tissue-specific stem cells gave rise to multicellular living systems with distinct organs which perform specific physiological functions. This setting is a constructive role of evolution; however, rebel cells can take over the molecular mechanisms for other purposes: nowadays we know that cancer stem cells, which generate aberrant organ-like structures, are at the top of a hierarchy. Furthermore, cancer stem cells are the root of metastasis, therapy resistance, and relapse. At present, most therapeutic drugs are unable to target cancer stem cells and therefore, treatment becomes a challenging issue. We expect that future research will uncover the mechanistic "forces" driving organ growth, paving the way to the implementation of new strategies to impair human tumorigenesis.

Stability of Pattern Formation in Systems with Dynamic Source Regions

We explain the principles of gene expression pattern stabilization in systems of interacting, diffusible morphogens, with dynamically established source regions. Using a reaction-diffusion model with a step-function production term, we identify the phase transition between low-precision indeterminate patterning and the phase in which a traveling, well-defined contact zone between two domains is formed. Our model analytically explains single- and two-gene domain dynamics and provides pattern stability conditions for all possible two-gene regulatory network motifs.

Universal dynamics of biological pattern formation in spatio-temporal morphogen variations

In biological systems, chemical signals termed morphogens self-organize into patterns that are vital for many physiological processes. As observed by Turing in 1952, these patterns are in a state of continual development, and are usually transitioning from one pattern into another. How do cells robustly decode these spatio-temporal patterns into signals in the presence of confounding effects caused by unpredictable or heterogeneous environments? Here, we answer this question by developing a general theory of pattern formation in spatio-temporal variations of ‘pre-pattern’ morphogens, which determine gene-regulatory network parameters. Through mathematical analysis, we identify universal dynamical regimes that apply to wide classes of biological systems. We apply our theory to two paradigmatic pattern-forming systems, and predict that they are robust with respect to non-physiological morphogen variations. More broadly, our theoretical framework provides a general approach to classify the emergent dynamics of pattern-forming systems based on how the bifurcations in their governing equations are traversed.

Characterizing the Impact of Communication on Cellular and Collective Behavior Using a Three-Dimensional Multiscale Cellular Model

Communication between cells enables the coordination that drives structural and functional complexity in biological systems. Both single and multicellular organisms have evolved diverse communication systems for a range of purposes, including synchronization of behavior, division of labor, and spatial organization. Synthetic systems are also increasingly being engineered to utilize cell-cell communication. While research has elucidated the form and function of cell-cell communication in many biological systems, our knowledge is still limited by the confounding effects of other biological phenomena at play and the bias of the evolutionary background. In this work, our goal is to push forward the context-free understanding of what impact cell-cell communication can have on cellular and population behavior to more fully understand the extent to which cell-cell communication systems can be utilized, modified, and engineered. We use an in silico model of 3D multiscale cellular populations, with dynamic intracellular networks interacting via diffusible signals. We focus on two key communication parameters: the effective interaction distance at which cells are able to interact and the receptor activation threshold. We found that cell-cell communication can be divided into six different forms along the parameter axes, three asocial and three social. We also show that cellular behavior, tissue composition, and tissue diversity are all highly sensitive to both the general form and specific parameters of communication even when the cellular network has not been biased towards that behavior.

To fit or not to fit: death decisions from morphogen fields

The transforming growth factor-β (TGF-β)-type morphogens are conserved throughout the animal kingdom. TGF-β-type molecules form spatial concentration gradients whose length scales with the size of growing, developing organs. Scaling of these morphogens can also be mediated by death, adjusting the size of the tissue to the range of the gradient. Death-mediated scaling might provide a molecular toolbox exploited by cancer cells.

Shaping the scaling characteristics of gap gene expression patterns in Drosophila

How patterns are formed to scale with tissue size remains an unresolved problem. Here we investigate embryonic patterns of gap gene expression along the anterior-posterior (AP) axis in Drosophila. We use embryos that greatly differ in length and, importantly, possess distinct length-scaling characteristics of the Bicoid (Bcd) gradient. We systematically analyze the dynamic movements of gap gene expression boundaries in relation to both embryo length and Bcd input as a function of time. We document the process through which such dynamic movements drive both an emergence of a global scaling landscape and evolution of boundary-specific scaling characteristics. We show that, despite initial differences in pattern scaling characteristics that mimic those of Bcd in the anterior, such characteristics of final patterns converge. Our study thus partitions the contributions of Bcd input and regulatory dynamics inherent to the AP patterning network in shaping embryonic pattern's scaling characteristics.

Orchestration of tissue shape changes and gene expression patterns in development

In development, tissue shape changes and gene expression patterns give rise to morphogenesis. Understanding tissue shape changes requires the analysis of mechanical properties of the tissue such as tissue rigidity, cell influx from neighboring tissues, cell shape changes and cell proliferation. Local and global gene expression patterns can be influenced by neighbor exchange and tissue shape changes. Here we review recent studies on the mechanisms for tissue elongation and its influences on dynamic gene expression patterns by focusing on vertebrate somitogenesis. We first introduce mechanical and biochemical properties of the segmenting tissue that drive tissue elongation. Then, we discuss patterning in the presence of cell mixing, scaling of signaling gradients, and dynamic phase waves of rhythmic gene expression under tissue shape changes. We also highlight the importance of theoretical approaches to address the relation between tissue shape changes and patterning.

Azot expression in the Drosophila gut modulates organismal lifespan

Cell Competition emerged in Drosophila as an unexpected phenomenon, when confronted clones of fit vs unfit cells genetically induced. During the last decade, it has been shown that this mechanism is physiologically active in Drosophila and higher organisms. In Drosophila, Flower (Fwe) eliminates unfit cells during development, regeneration and disease states. Furthermore, studies suggest that Fwe signaling is required to eliminate accumulated unfit cells during adulthood extending Drosophila lifespan. Indeed, ahuizotl (azot) mutants accumulate unfit cells during adulthood and after physical insults in the brain and other epithelial tissues, showing a decrease in organismal lifespan. On the contrary, flies carrying three functional copies of the gene, unfit cell culling seems to be more efficient and show an increase in lifespan. During aging, Azot is required for the elimination of unfit cells, however, the specific organs modulating organismal lifespan by Azot remain unknown. Here we found a potential connection between gut-specific Azot expression and lifespan which may uncover a more widespread organ-specific mechanism modulating organismal survival.

Coupling cell proliferation rates to the duration of recruitment controls final size of the Drosophila wing

Organ growth driven by cell proliferation is an exponential process. As a result, even small variations in proliferation rates, when integrated over a relatively long developmental time, will lead to large differences in size. How organs robustly control their final size despite perturbations in cell proliferation rates throughout development is a long-standing question in biology. Using a mathematical model, we show that in the developing wing of the fruit fly, Drosophila melanogaster, variations in proliferation rates of wing-committed cells are inversely proportional to the duration of cell recruitment, a differentiation process in which a population of undifferentiated cells adopt the wing fate by expressing the selector gene, vestigial. A time-course experiment shows that vestigial-expressing cells increase exponentially while recruitment takes place, but slows down when recruitable cells start to vanish, suggesting that undifferentiated cells may be driving proliferation of wing-committed cells. When this observation is incorporated in our model, we show that the duration of cell recruitment robustly determines a final wing size even when cell proliferation rates of wing-committed cells are perturbed. Finally, we show that this control mechanism fails when perturbations in proliferation rates affect both wing-committed and recruitable cells, providing an experimentally testable hypothesis of our model.

Patterning principles of morphogen gradients

Metazoan embryos develop from a single cell into three-dimensional structured organisms while groups of genetically identical cells attain specialized identities. Cells of the developing embryo both create and accurately interpret morphogen gradients to determine their positions and make specific decisions in response. Here, we first cover intellectual roots of morphogen and positional information concepts. Focusing on animal embryos, we then provide a review of current understanding on how morphogen gradients are established and how their spans are controlled. Lastly, we cover how gradients evolve in time and space during development, and how they encode information to control patterning. In sum, we provide a list of patterning principles for morphogen gradients and review recent advances in quantitative methodologies elucidating information provided by morphogens.

Early patterning followed by tissue growth establishes distal identity in Drosophila Malpighian tubules

Specification and elaboration of proximo-distal (P-D) axes for structures or tissues within a body occurs secondarily from that of the main axes of the body. Our understanding of the mechanism(s) that pattern P-D axes is limited to a few examples such as vertebrate and invertebrate limbs. Drosophila Malpighian/renal tubules (MpTs) are simple epithelial tubules, with a defined P-D axis. How this axis is patterned is not known, and provides an ideal context to understand patterning mechanisms of a secondary axis. Furthermore, epithelial tubules are widespread, and their patterning is not well understood. Here, we describe the mechanism that establishes distal tubule and show this is a radically different mechanism to that patterning the proximal MpT. The distal domain is patterned in two steps: distal identity is specified in a small group of cells very early in MpT development through Wingless/Wnt signalling. Subsequently, this population is expanded by proliferation to generate the distal MpT domain. This mechanism enables distal identity to be established in the tubule in a domain of cells much greater than the effective range of Wingless.

Long-range morphogen gradient formation by cell-to-cell signal propagation

Morphogen gradients are a central concept in developmental biology. Their formation often involves the secretion of morphogens from a local source, that spread by diffusion in the cell field, where molecules eventually get degraded. This implies limits to both the time and length scales over which morphogen gradients can form which are set by diffusion coefficients and degradation rates. Towards the goal of identifying plausible mechanisms capable of extending the gradient range, we here use theory to explore properties of a cell-to-cell signaling relay. Inspired by the millimeter-scale Wnt-expression and signaling gradients in flatworms, we consider morphogen-mediated morphogen production in the cell field. We show that such a relay can generate stable morphogen and signaling gradients that are oriented by a local, morphogen-independent source of morphogen at a boundary. This gradient formation can be related to an effective diffusion and an effective degradation that result from morphogen production due to signaling relay. If the secretion of morphogen produced in response to the relay is polarized, it further gives rise to an effective drift. We find that signaling relay can generate long-ranged gradients in relevant times without relying on extreme choices of diffusion coefficients or degradation rates, thus exceeding the limits set by physiological diffusion coefficients and degradation rates. A signaling relay is hence an attractive principle to conceptualize long-range gradient formation by slowly diffusing morphogens that are relevant for patterning in adult contexts such as regeneration and tissue turn-over.

Relationship between epithelial organization and morphogen interpretation

Despite molecular noise and genetic differences between individuals, developmental outcomes are remarkably constant. Decades of research has focused on the underlying mechanisms that ensure this precision and robustness. Recent quantifications of chemical gradients and epithelial cell shapes provide novel insights into the basis of precise development. In this review, we argue that these two aspects may be linked in epithelial morphogenesis.

Mechanical constraints to cell-cycle progression in a pseudostratified epithelium

As organs and tissues approach their normal size during development or regeneration, growth slows down, and cell proliferation progressively comes to a halt. Among the various processes suggested to contribute to growth termination,1-10 mechanical feedback, perhaps via adherens junctions, has been suggested to play a role.11-14 However, since adherens junctions are only present in a narrow plane of the subapical region, other structures are likely needed to sense mechanical stresses along the apical-basal (A-B) axis, especially in a thick pseudostratified epithelium. This could be achieved by nuclei, which have been implicated in mechanotransduction in tissue culture.15 In addition, mechanical constraints imposed by nuclear crowding and spatial confinement could affect interkinetic nuclear migration (IKNM),16 which allows G2 nuclei to reach the apical surface, where they normally undergo mitosis.17-25 To explore how mechanical constraints affect IKNM, we devised an individual-based model that treats nuclei as deformable objects constrained by the cell cortex and the presence of other nuclei. The model predicts changes in the proportion of cell-cycle phases during growth, which we validate with the cell-cycle phase reporter FUCCI (Fluorescent Ubiquitination-based Cell Cycle Indicator).26 However, this model does not preclude indefinite growth, leading us to postulate that nuclei must migrate basally to access a putative basal signal required for S phase entry. With this refinement, our updated model accounts for the observed progressive slowing down of growth and explains how pseudostratified epithelia reach a stereotypical thickness upon completion of growth.

ECM degradation in the Drosophila abdominal epidermis initiates tissue growth that ceases with rapid cell-cycle exit

During development, multicellular organisms undergo stereotypical patterns of tissue growth in space and time. How developmental growth is orchestrated remains unclear, largely due to the difficulty of observing and quantitating this process in a living organism. Drosophila histoblast nests are small clusters of progenitor epithelial cells that undergo extensive growth to give rise to the adult abdominal epidermis and are amenable to live imaging. Our quantitative analysis of histoblast proliferation and tissue mechanics reveals that tissue growth is driven by cell divisions initiated through basal extracellular matrix degradation by matrix metalloproteases secreted by the neighboring larval epidermal cells. Laser ablations and computational simulations show that tissue mechanical tension does not decrease as the histoblasts fill the abdominal epidermal surface. During tissue growth, the histoblasts display oscillatory cell division rates until growth termination occurs through the rapid emergence of G0/G1 arrested cells, rather than a gradual increase in cell-cycle time as observed in other systems such as the Drosophila wing and mouse postnatal epidermis. Different developing tissues can therefore achieve their final size using distinct growth termination strategies. Thus, adult abdominal epidermal development is characterized by changes in the tissue microenvironment and a rapid exit from the cell cycle.

A role for Flower and cell death in controlling morphogen gradient scaling

During development, morphogen gradients encode positional information to pattern morphological structures during organogenesis¹. Some gradients, like that of Dpp in the fly wing, remain proportional to the size of growing organs-that is, they scale. Gradient scaling keeps morphological patterns proportioned in organs of different sizes^2,3. Here we show a mechanism of scaling that ensures that, when the gradient is smaller than the organ, cell death trims the developing tissue to match the size of the gradient. Scaling is controlled by molecular associations between Dally and Pentagone, known factors involved in scaling, and a key factor that mediates cell death, Flower^4-6. We show that Flower activity in gradient expansion is not dominated by cell death, but by the activity of Dally/Pentagone on scaling. Here we show a potential connection between scaling and cell death that may uncover a molecular toolbox hijacked by tumours.

Ecdysone coordinates plastic growth with robust pattern in the developing wing

Animals develop in unpredictable, variable environments. In response to environmental change, some aspects of development adjust to generate plastic phenotypes. Other aspects of development, however, are buffered against environmental change to produce robust phenotypes. How organ development is coordinated to accommodate both plastic and robust developmental responses is poorly understood. Here, we demonstrate that the steroid hormone ecdysone coordinates both plasticity of organ size and robustness of organ pattern in the developing wings of the fruit fly Drosophila melanogaster. Using fed and starved larvae that lack prothoracic glands, which synthesize ecdysone, we show that nutrition regulates growth both via ecdysone and via an ecdysone-independent mechanism, while nutrition regulates patterning only via ecdysone. We then demonstrate that growth shows a graded response to ecdysone concentration, while patterning shows a threshold response. Collectively, these data support a model where nutritionally regulated ecdysone fluctuations confer plasticity by regulating disc growth in response to basal ecdysone levels and confer robustness by initiating patterning only once ecdysone peaks exceed a threshold concentration. This could represent a generalizable mechanism through which hormones coordinate plastic growth with robust patterning in the face of environmental change.

Precision of morphogen gradients in neural tube development

Morphogen gradients encode positional information during development. How high patterning precision is achieved despite natural variation in both the morphogen gradients and in the readout process, is still largely elusive. Here, we show that the positional error of gradients in the mouse neural tube has previously been overestimated, and that the reported accuracy of the central progenitor domain boundaries in the mouse neural tube can be achieved with a single gradient, rather than requiring the simultaneous readout of opposing gradients. Consistently and independently, numerical simulations based on measured molecular noise levels likewise result in lower gradient variabilities than reported. Finally, we show that the patterning mechanism yields progenitor cell numbers with even greater precision than boundary positions, as gradient amplitude changes do not affect interior progenitor domain sizes. We conclude that single gradients can yield the observed developmental precision, which provides prospects for tissue engineering.

Avalanches during epithelial tissue growth; Uniform Growth and a drosophila eye disc model

Epithelial tissues constitute an exotic type of active matter with non-linear properties reminiscent of amorphous materials. In the context of a proliferating epithelium, modeled by the quasistatic vertex model, we identify novel discrete tissue scale rearrangements, i.e. cellular rearrangement avalanches, which are a form of collective cell movement. During the avalanches, the vast majority of cells retain their neighbors, and the resulting cellular trajectories are radial in the periphery, a vortex in the core. After the onset of these avalanches, the epithelial area grows discontinuously. The avalanches are found to be stochastic, and their strength is correlated with the density of cells in the tissue. Overall, avalanches redistribute accumulated local spatial pressure along the tissue. Furthermore, the distribution of avalanche magnitudes is found to obey a power law, with an exponent consistent with sheer induced avalanches in amorphous materials. To understand the role of avalanches in organ development, we simulate epithelial growth of the Drosophila eye disc during the third instar using a computational model, which includes both chemical and mechanistic signaling. During the third instar, the morphogenetic furrow (MF), a ~10 cell wide wave of apical area constriction propagates through the epithelium. These simulations are used to understand the details of the growth process, the effect of the MF on the growth dynamics on the tissue scale, and to make predictions for experimental observations. The avalanches are found to depend on the strength of the apical constriction of cells in the MF, with a stronger apical constriction leading to less frequent and more pronounced avalanches. The results herein highlight the dependence of simulated tissue growth dynamics on relaxation timescales, and serve as a guide for in vitro experiments.

The wing imaginal disc

The Drosophila wing imaginal disc is a tissue of undifferentiated cells that are precursors of the wing and most of the notum of the adult fly. The wing disc first forms during embryogenesis from a cluster of ∼30 cells located in the second thoracic segment, which invaginate to form a sac-like structure. They undergo extensive proliferation during larval stages to form a mature larval wing disc of ∼35,000 cells. During this time, distinct cell fates are assigned to different regions, and the wing disc develops a complex morphology. Finally, during pupal stages the wing disc undergoes morphogenetic processes and then differentiates to form the adult wing and notum. While the bulk of the wing disc comprises epithelial cells, it also includes neurons and glia, and is associated with tracheal cells and muscle precursor cells. The relative simplicity and accessibility of the wing disc, combined with the wealth of genetic tools available in Drosophila, have combined to make it a premier system for identifying genes and deciphering systems that play crucial roles in animal development. Studies in wing imaginal discs have made key contributions to many areas of biology, including tissue patterning, signal transduction, growth control, regeneration, planar cell polarity, morphogenesis, and tissue mechanics.

Size matters: tissue size as a marker for a transition between reaction-diffusion regimes in spatio-temporal distribution of morphogens

The reaction-diffusion model constitutes one of the most influential mathematical models to study distribution of morphogens in tissues. Despite its widespread use, the effect of finite tissue size on model-predicted spatio-temporal morphogen distributions has not been completely elucidated. In this study, we analytically investigated the spatio-temporal distributions of morphogens predicted by a reaction-diffusion model in a finite one-dimensional domain, as a proxy for a biological tissue, and compared it with the solution of the infinite-domain model. We explored the reduced parameter, the tissue length in units of a characteristic reaction-diffusion length, and identified two reaction-diffusion regimes separated by a crossover tissue size estimated in approximately three characteristic reaction-diffusion lengths. While above this crossover the infinite-domain model constitutes a good approximation, it breaks below this crossover, whereas the finite-domain model faithfully describes the entire parameter space. We evaluated whether the infinite-domain model renders accurate estimations of diffusion coefficients when fitted to finite spatial profiles, a procedure typically followed in fluorescence recovery after photobleaching (FRAP) experiments. We found that the infinite-domain model overestimates diffusion coefficients when the domain is smaller than the crossover tissue size. Thus, the crossover tissue size may be instrumental in selecting the suitable reaction-diffusion model to study tissue morphogenesis.