Mathematical Model of the Formation of Morphogen Gradients Through Membrane-Associated Non-receptors

The importance of morphogens is a central concept in developmental biology. Multiple-fate patterning and the robustness of the morphogen gradient are essential for embryo development. The ways by which morphogens diffuse from a local source to form long distance gradients can differ from one morphogen to the other, and for the same morphogen in different organs. This paper will study the mechanism by which morphogens diffuse through the aid of membrane-associated non-receptors and will investigate how the membrane-associated non-receptors help the morphogen to form long distance gradients and to achieve good robustness. Such a mechanism has been reported for some morphogens that are rapidly turned over. We will establish a set of reaction-diffusion equations to model the dynamical process of morphogen gradient formation. Under the assumption of rapid morphogen degradation, we discuss the existence, uniqueness, local stability, approximation solution, and the robustness of the steady-state gradient. The results in this paper show that when the morphogen is rapidly turned over, diffusion of the morphogen through membrane-associated non-receptors is a possible strategy to form a long distance multiple-fate gradient that is locally stable and is robust against the changes in morphogen synthesis rate.     

BMP morphogen gradients in flies

Bone morphogenetic proteins (BMPs) act as morphogens to control patterning and growth in a variety of developing tissues in different species. How BMP morphogen gradients are established and interpreted in the target tissues has been extensively studied in Drosophila melanogaster. In Drosophila, Decapentaplegic (Dpp), a homologue of vertebrate BMP2/4, acts as a morphogen to control dorsal–ventral patterning of the early embryo and anterior–posterior patterning and growth of the wing imaginal disc. Despite intensive efforts over the last twenty years, how the Dpp morphogen gradient in the wing imaginal disc forms remains controversial, while gradient formation in the early embryo is well understood. In this review, we first focus on the current models of Dpp morphogen gradient formation in these two tissues, and then discuss new strategies using genome engineering and nanobodies to tackle open questions.     

Read-Out of Dynamic Morphogen Gradients on Growing Domains

Quantitative data from the Drosophila wing imaginal disc reveals that the amplitude of the Decapentaplegic (Dpp) morphogen gradient increases continuously. It is an open question how cells can determine their relative position within a domain based on a continuously increasing gradient. Here we show that pre-steady state diffusion-based dispersal of morphogens results in a zone within the growing domain where the concentration remains constant over the patterning period. The position of the zone that is predicted based on quantitative data for the Dpp morphogen corresponds to where the Dpp-dependent gene expression boundaries of spalt (sal) and daughters against dpp (dad) emerge. The model also suggests that genes that are scaling and are expressed at lateral positions are either under the control of a different read-out mechanism or under the control of a different morphogen. The patterning mechanism explains the extraordinary robustness that is observed for variations in Dpp production, and offers an explanation for the dual role of Dpp in controlling patterning and growth. Pre-steady-state dynamics are pervasive in morphogen-controlled systems, thus making this a probable general mechanism for the scaled read-out of morphogen gradients in growing developmental systems.     

Fat facets deubiquitylation of Medea/Smad4 modulates interpretation of a Dpp morphogen gradient

The ability of secreted Transforming Growth Factor β (TGFβ) proteins to act as morphogens dictates that their influence be strictly regulated. Here, we report that maternally contributed fat facets (faf; a homolog of USP9X/FAM) is essential for proper interpretation of the zygotic Decapentaplegic (Dpp) morphogen gradient that patterns the embryonic dorsal-ventral axis. The data suggest that the loss of faf reduces the activity of Medea (a homolog of Smad4) below the minimum necessary for adequate Dpp signaling and that this is likely due to excessive ubiquitylation on a specific lysine. This study supports the hypothesis that the control of cellular responsiveness to TGFβ signals at the level of Smad4 ubiquitylation is a conserved mechanism required for proper implementation of a morphogen gradient.     

Formation and maintenance of morphogen gradients: an essential role for the endomembrane system in Drosophila melanogaster wing development

As early as 1964 it was suggested that simple diffusion of morphogens away from their secretion source did not provide an adequate explanation for the formation and maintenance of morphogen gradients. Involvement of the endosome in morphogen distribution models provides an explanation for the slow, directional movement of morphogens, as well as their ability to form intracellular and extracellular gradients independent of morphogen production rates. Drosophila melanogaster morphogens Wg and Dpp form stable, steep, long-range gradients that specify the polarity of the wing disc. The process of endocytosis is imperative to the two central themes in gradient formation: active transport facilitating long-range signaling and degradation of morphogen to sustain gradient shape. This review investigates the endomembrane-mediated processes of re-secretion, degradation and argosome transport of Wg and Dpp in the hope that a better understanding of the endomembrane system will contribute to a more accurate and comprehensive model for morphogen gradient formation and maintenance.     

The Role of Endocytosis during Morphogenetic Signaling

Morphogens are signaling molecules that are secreted by a localized source and spread in a target tissue where they are involved in the regulation of growth and patterning. Both the activity of morphogenetic signaling and the kinetics of ligand spreading in a tissue depend on endocytosis and intracellular trafficking. Here, we review quantitative approaches to study how large-scale morphogen profiles and signals emerge in a tissue from cellular trafficking processes and endocytic pathways. Starting from the kinetics of endosomal networks, we discuss the role of cellular trafficking and receptor dynamics in the formation of morphogen gradients. These morphogen gradients scale during growth, which implies that overall tissue size influences cellular trafficking kinetics. Finally, we discuss how such morphogen profiles can be used to control tissue growth. We emphasize the role of theory in efforts to bridge between scales.A fundamental challenge in biology is to understand how morphologies and complex patterns form in multicellular systems by the collective organization of many cells. Cells divide and undergo apoptosis, and they communicate via signaling pathways that use molecules as information carriers. In tissues, large-scale patterns of gene expression emerge from the coordinated signaling activity and response of many cells. The establishment of such patterns is often guided by long-range concentration profiles of morphogens. Cell divisions and cell rearrangements must be coordinated over large distances to achieve specific tissue sizes and shapes. To unravel how molecular processes and interactions can eventually be responsible for the formation of structures and patterns in tissues during development, it is important to study processes at different scales and understand how different levels of organization are connected. Such an approach becomes strongest if it involves a combination of quantitative experimental studies with theory.In the present article, we discuss several such approaches on different scales with a particular emphasis on theory. Starting from the kinetic and dynamic properties of endosomal networks inside a cell, we discuss transport processes in a tissue that can be related to kinetic trafficking parameters. Such transport processes are then responsible for the formation of graded morphogen concentration profiles. To permit scalable patterns in tissues of different sizes, it has been suggested that morphogen gradients scale during growth. This can be achieved on the tissue level by feedback systems that are sensitive to tissue size and regulate, for example, morphogen degradation. Finally, morphogen gradients that scale with tissue size can provide a system to robustly organize cell division in a large tissue and generate homogeneous growth. Theory can play an important role to bridge scales and understand how molecular and cellular processes can control pattern formation and tissue growth on larger scales.Morphogens are signaling molecules that are secreted in specific regions of developing tissues and can induce signaling activity far from their source. They typically form graded concentration profiles and therefore endow cells with positional information (cells can obtain information about their position in a tissue). Thus, they can guide cells to differentiate into complex morphological patterns. Morphogens also control cell growth and cell division. Because they control both patterning and growth, they may play a key role to coordinate these two processes. Such coordination is important because the size of morphological patterns must adjust during growth, whereas growth influences such patterns. A well-studied morphogen is Decapentaplegic (Dpp), which controls morphogenesis in the imaginal wing disc of developing Drosophila. Consequently, mutations in Dpp or defects in the trafficking pathways that control its graded concentration profiles and signaling affect the formation and structure of the adult wing.The study of morphogens was traditionally approached from a genetic perspective: Which gene products behave like morphogens? Which mutants affect patterning and growth? The realization that morphogens typically operate by a gradient of concentration raised the question of how morphogen gradients are generated. It became clear that the cellular trafficking of morphogens is a key issue for the generation of morphogen profiles. Morphogens are secreted ligands that bind receptors in the plasma membrane. The secretion of the ligands and the concentrations of receptor, ligand, and receptor/ligand complex at the plasma membrane are governed by their trafficking in the cell by vesicular transport. In particular, it was shown that trafficking through the endocytic pathway has an important impact on the formation of morphogen gradients (reviewed in Gonzalez-Gaitan 2003; see Bökel and Brand 2014). This is, to a large extent, how the cells respond to morphogens and contribute to set their local concentrations. To understand functions of morphogens in a tissue, we need to study how the gradient is formed. This, in turn, requires insights into morphogen trafficking through the endocytic pathway. The problem of morphogen behavior, therefore, becomes a problem spanning several levels of complexity: the organ level, the tissue level, the cell level, the organelle level, and the molecular level. Theoretical approaches motivated by physics combined with quantitative experimental approaches provide an ideal framework to understand how these different levels of complexity are intertwined.Two recent discoveries highlighted such integration. (1) The observation that profiles of the morphogen Dpp scale during growth, which implies that the rate of Dpp degradation mediated by the endocytic pathway of each of the cells in the tissue depends on the size of the overall tissue. This suggests that two levels of complexity are linked because cellular trafficking receives cues about the global tissue size. (2) As a result of the changes of the degradation rate that leads to gradient scaling, cells receive an increasing level of signaling. This, in turn, can be used by the cells to decide when to divide. This regulation again involves two levels of complexity because regulation at the endocytic pathway determines the growth properties of the tissue and, ultimately, its final size.In the following, we discuss quantitative approaches to study cellular signaling processes on different scales. Here, the aim is to understand how patterns on large scales can emerge during development from molecular processes and signaling pathways that involve endocytosis and cellular trafficking. We begin by describing trafficking of ligands in the endocytic pathway. We then consider the situation of a morphogen ligand and its impact in gradient formation. Subsequently, we discuss how gradient scaling might be realized. Finally, we discuss how such scaling processes play an important role in the regulation of morphogenetic growth.     

Formation and maintenance of morphogen gradients: An essential role for the endomembrane system in Drosophila melanogaster wing development

As early as 1964 it was suggested that simple diffusion of morphogens away from their secretion source did not provide an adequate explanation for the formation and maintenance of morphogen gradients. Involvement of the endosome in morphogen distribution models provides an explanation for the slow, directional movement of morphogens, as well as their abilty to form intracellular and extracellular gradients independent of morphogen production rates. Drosophila melanogaster morphogens Wg and Dpp form stable, steep, long-range gradients that specify the polarity of the wing disc. The process of endocytosis is imparative to the two central themes in gradient formation; active transport facilitating long-range signalling, and degradation of morphogen to sustain gradient shape. This review investigates the endomembrane mediated processes of re-secretion, degradation, and argosome transport of Wg and Dpp in the hope that a better understanding of the endomembrane system will contribute to a more accurate and comprehensive model for morphogen gradient formation and maintenance.     

Membrane-Associated Non-Receptors and Morphogen Gradients

A previously investigated basic model (System B) for the study of signaling morphogen gradient formation that allows for reversible binding of morphogens (aka ligands) with signaling receptors, degradation of bound morphogens and diffusion of unbound morphogens is extended to include the effects of membrane-bound non-signaling molecules (or non-receptors for short) such as proteoglycans that bind reversibly with the same morphogens and degrade them. Our main goal is to delineate the effects of the presence of non-receptors on the existence and properties of the steady-state concentration gradient of signaling ligand–receptor complexes. Stability of the steady-state morphogen gradients is established and the time to reach steady-state behavior after the onset of morphogen production will be analyzed. The theoretical findings offer explanations for observations reported in several previous experiments on Drosophila wing imaginal discs.     

Wingless gradient formation in the Drosophila wing

BACKGROUND: Secreted signaling proteins of the Wingless (Wg)/Wnt, Hedgehog and bone morphogenetic protein (BMP)/Decapentaplegic (Dpp) families function as morphogens to control growth and pattern formation during development. Although these proteins have been shown to act directly on distant cells in the developing limbs of the fruit fly Drosophila, little is known about how ligand gradients form in vivo. Wg protein is found in vesicles in Wg-responsive cells in the embryo and imaginal discs. It has been proposed that Wg may be transported by a vesicle-mediated mechanism. RESULTS: A novel method to visualize extracellular Wg protein was used to show that Wg forms an unstable gradient on the basolateral surface of the wing imaginal disc epithelium. Wg movement did not require internalization by dynamin-mediated endocytosis. Dynamin activity was, however, required for Wg secretion. By reversibly blocking Wg secretion, we found that Wg moves rapidly to form a long-range extracellular gradient. CONCLUSIONS: The Wg morphogen gradient forms by rapid movement of ligand through the extracellular space, and depends on continuous secretion and rapid turnover. Endocytosis is not required for Wg movement, but contributes to shaping the gradient by removing extracellular Wg. We propose that the extracellular Wg gradient forms by diffusion.     

Three Drosophila EXT genes shape morphogen gradients through synthesis of heparan sulfate proteoglycans

The signaling molecules Hedgehog (Hh), Decapentaplegic (Dpp) and Wingless (Wg) function as morphogens and organize wing patterning in Drosophila. In the screen for mutations that alter the morphogen activity, we identified novel mutants of two Drosophila genes, sister of tout-velu (sotv) and brother of tout-velu (botv), and new alleles of tout-velu (ttv). The encoded proteins of these genes belong to an EXT family of proteins that have or are closely related to glycosyltransferase activities required for biosynthesis of heparan sulfate proteoglycans (HSPGs). Mutation in any of these genes impaired biosynthesis of HSPGs in vivo, indicating that, despite their structural similarity, they are not redundant in the HSPG biosynthesis. Protein levels and signaling activities of Hh, Dpp and Wg were reduced in the cells mutant for any of these EXT genes to a various degree, Wg signaling being the least sensitive. Moreover, all three morphogens were accumulated in the front of EXT mutant cells, suggesting that these morphogens require HSPGs to move efficiently. In contrast to previous reports that ttv is involved exclusively in Hh signaling, we found that ttv mutations also affected Dpp and Wg. These data led us to conclude that each of three EXT genes studied contribute to Hh, Dpp and Wg morphogen signaling. We propose that HSPGs facilitate the spreading of morphogens and therefore, function to generate morphogen concentration gradients.     

Regulation of cell proliferation by a morphogen gradient

One model to explain the relationship between patterning and growth during development posits that growth is regulated by the slope of morphogen gradients. The Decapentaplegic (DPP) morphogen controls growth in the Drosophila wing, but the slope of the DPP activity gradient has not been shown to influence growth. By employing a method for spatial, temporal, and quantitative control over gene expression, we show that the juxtaposition of cells perceiving different levels of DPP signaling is essential for medial-wing-cell proliferation and can be sufficient to promote the proliferation of cells throughout the wing. Either activation or inhibition of the DPP pathway in clones at levels distinct from those in surrounding cells stimulates nonautonomous cell proliferation. Conversely, uniform activation of the DPP pathway inhibits cell proliferation in medial wing cells. Our observations provide a direct demonstration that the slope of a morphogen gradient regulates growth during development.     

Spatiotemporal mechanisms of morphogen gradient interpretation

Few mechanistic ideas from the pre-molecular era of biology have had as enduring an impact as the morphogen concept. In the classical view, cells in developing embryos obtain positional information by measuring morphogen concentrations and comparing them with fixed concentration thresholds; as a result, graded morphogen distributions map into discrete spatial arrangements of gene expression. Recent studies on Hedgehog and other morphogens suggest that establishing patterns of gene expression may be less a function of absolute morphogen concentrations, than of the dynamics of signal transduction, gene expression, and gradient formation. The data point away from any universal model of morphogen interpretation and suggest that organisms use multiple mechanisms for reading out developmental signals in order to accomplish specific patterning goals.     

Formation of a functional morphogen gradient by a passive process in tissue from the early Xenopus embryo

In early development much of the cellular diversity and pattern formation of the embryo is believed to be set up by morphogens. However, for many morphogens, including members of the TGF-beta superfamily, the mechanism(s) by which they reach distant cells is unknown. We have used immunofluorescence to detect, at single cell resolution, a morphogen gradient formed across vertebrate tissue. The TGF-beta ligand is distributed in a gradient visible up to 7 cell diameters (about 150-200 microm) from its source, and is detectable only in the extracellular space. This morphogen gradient is functional, since we demonstrate activation of a high response gene (Xeomes) and a low-response gene (Xbra) at different distances from the TGF-beta source. Expression of the high affinity type II TGF-beta receptor is necessary for detection of the gradient, but the shape of the gradient formed only depends in part on the spatial variation in the amount of receptor. Finally, we demonstrate that the molecular processes that participate in forming this functional morphogen gradient are temperature independent, since the gradient forms to a similar extent whether the cells are maintained at 4 degrees C or 23 degrees C. In contrast, TGF-beta1 internalisation by cells of the Xenopus embryo is a temperature-dependent process. Our results thus suggest that neither vesicular transcytosis nor other active processes contribute to a significant extent to the formation of the morphogen gradient we observe. We conclude that, in the model system used here, a functional morphogen gradient can be formed within a few hours by a mechanism of passive diffusion.     

Genetics of morphogen gradients

The organization of cells and tissues is controlled by the action of 'form-giving' signalling molecules, or morphogens, which pattern a developmental field in a concentration-dependent manner. As the fate of each cell in the field depends on the level of the morphogen signal, the concentration gradient of the morphogen prefigures the pattern of development. In recent years, molecular genetic studies in Drosophila melanogaster have allowed tremendous progress in understanding how morphogen gradients are formed and maintained, and the mechanism by which receiving cells respond to the gradient.     

器官成形素调控果蝇翅芽细胞形貌的研究进展

果蝇翅芽是研究细胞形貌发生的模式系统。在果蝇翅芽的发育过程中,器官成形素由浓度高的区域(成形素表达细胞)向浓度低的区域(接收细胞)移动,形成动态的浓度梯度。器官成形素信号通路的激活调控翅芽细胞的形貌发生、存活、生长和分化。目前已鉴定的在翅芽细胞表达的器官成形素包括Hedgehog(Hh),Decapentaplegic(Dpp)和Wingless(Wg)。结合国际最新研究进展,本文综述了3种器官成形素在翅芽细胞形貌发生过程中的重要作用,讨论了细胞形貌发生的分子机制。     

A mechanism for the sharp transition of morphogen gradient interpretation in <Emphasis Type="Italic">Xenopus</Emphasis>

Background  

One way in which positional information is established during embryonic development is through the graded distribution of diffusible morphogens. Unfortunately, little is known about how cells interpret different concentrations of morphogen to activate different genes or how thresholds are generated in a morphogen gradient.     

On the role of glypicans in the process of morphogen gradient formation

Glypicans are cell surface molecules that influence signaling and gradient formation of secreted morphogens and growth factors. Several distinct functions have been ascribed to glypicans including acting as co-receptors for signaling proteins. Recent data show that glypicans are also necessary for morphogen propagation in the tissue. In the present study, a model describing the interaction of a morphogen with glypicans is formulated, analyzed and compared with measurements of the effect of glypican Dally-like (Dlp) overexpression on Wingless (Wg) morphogen signaling in Drosophila melanogaster wing imaginal discs. The model explains the opposing effect that Dlp overexpression has on Wg signaling in the distal and proximal regions of the disc and makes a number of quantitative predictions for further experiments. In particular, our model suggests that Dlp acts by allowing Wg to diffuse on cell surface while protecting it from loss and degradation, and that Dlp rather than acting as Wg co-receptor competes with receptors for morphogen binding.     

Distinct and collaborative roles of Drosophila EXT family proteins in morphogen signalling and gradient formation

Heparan sulfate proteoglycans (HSPG) have been implicated in regulating the signalling activities of secreted morphogen molecules including Wingless (Wg), Hedgehog (Hh) and Decapentaplegic (Dpp). HSPG consists of a protein core to which heparan sulfate (HS) glycosaminoglycan (GAG) chains are attached. The formation of HS GAG chains is catalyzed by glycosyltransferases encoded by members of the EXT family of putative tumor suppressors linked to hereditary multiple exostoses. Previous studies in Drosophila demonstrated that tout-velu (ttv), the Drosophila EXT1, is required for Hh movement. However, the functions of other EXT family members are unknown. We have identified and isolated the other two members of the Drosophila EXT family genes, which are named sister of tout-velu (sotv) and brother of tout-velu (botv), and encode Drosophila homologues of vertebrate EXT2 and EXT-like 3 (EXTL3), respectively. We show that both Hh and Dpp signalling activities, as well as their morphogen distributions, are defective in cells mutant for ttv, sotv or botv in the wing disc. Surprisingly, although Wg morphogen distribution is abnormal in ttv, sotv and botv, Wg signalling is only defective in botv mutants or ttv-sotv double mutants, and not in ttv nor sotv alone, suggesting that Ttv and Sotv are redundant in Wg signalling. We demonstrate further that Ttv and Sotv form a complex and are co-localized in vivo. Our results, along with previous studies on Ttv, provide evidence that all three Drosophila EXT proteins are required for the biosynthesis of HSPGs, and for the gradient formation of the Wg, Hh and Dpp morphogens. Our results also suggest that HSPGs have two distinct roles in Wg morphogen distribution and signalling.     

Shaping Morphogen Gradients by Proteoglycans

During development, secreted morphogens such as Wnt, Hedgehog (Hh), and BMP emit from their producing cells in a morphogenetic field, and specify different cell fates in a direct concentration-dependent manner. Understanding how morphogens form their concentration gradients to pattern tissues has been a central issue in developmental biology. Various experimental studies from Drosophila have led to several models to explain the formation of morphogen gradients. Over the past decade, one of the main findings in this field is the characterization of heparan sulfate proteoglycan (HSPG) as an essential regulator for morphogen gradient formation. Genetic and cell biological studies have showed that HSPGs can regulate morphogen activities at various steps including control of morphogen movement, signaling, and intracellular trafficking. Here, we review these data, highlighting recent findings that reveal mechanistic roles of HSPGs in controlling morphogen gradient formation.Embryonic development involves many spatial and temporal patterns of cell and tissue organization. These patterning processes are controlled by gradients of morphogens, the “form-generating substances” (Tabata and Takei 2004; Lander 2007). Secreted morphogen molecules, including members of Wnt, Hedgehog (Hh), and transforming growth factor-β (TGF-β) families, are generated from organizing centers and form concentration gradients to specify distinct cell fates in a concentration-dependent manner. Understanding how morphogen gradients are established during development has been a central question in developmental biology. Over the past decade, studies in both Drosophila and vertebrates have yielded important insights in this field. One of the important findings is the characterization of heparan sulfate proteoglycan (HSPG) as an essential regulator for morphogen gradient formation. In this review, we first discuss various models for morphogen movement. Then, we focus on the functions of HSPGs in morphogen movement, signaling, and trafficking.