Robust Generation and Decoding of Morphogen Gradients

Morphogen gradients play a key role in multiple differentiation processes. Both the formation of the gradient and its interpretation by the receiving cells need to occur at high precision to ensure reproducible patterning. This need for quantitative precision is challenged by fluctuations in the environmental conditions and by variations in the genetic makeup of the developing embryos. We discuss mechanisms that buffer morphogen profiles against variations in gene dosage. Self-enhanced morphogen degradation and pre-steady-state decoding provide general means for buffering the morphogen profile against fluctuations in morphogen production rate. A more specific “shuttling” mechanism, which establishes a sharp and robust activation profile of a widely expressed morphogen, and enables the adjustment of morphogen profile with embryo size, is also described. Finally, we consider the transformation of the smooth gradient profile into sharp borders of gene expression in the signal-receiving cells. The integration theory and experiments are increasingly used, providing key insights into the system-level functioning of the developmental system.In order for a uniform field of cells to differentiate into a reproducible pattern of organs and tissues, cells need to receive information about their position within the field. During development, positional information is often conveyed by spatial gradients of morphogens (Wolpert 1989). In the presence of such gradients, cells are subject to different levels of morphogen, depending on their positions within the field, and activate, accordingly, one of several gene expression cassettes. The quantitative shape of the morphogen gradient is critical for patterning, with cell-fate boundaries established at specific concentration thresholds. Although these general features of morphogen-based patterning are universal, the range and form of the morphogen profile, and the pattern of induced target genes, vary significantly depending on the tissue setting and the signaling pathways used.The formation of a morphogen gradient is a dynamic process, influenced by the kinetics of morphogen production, diffusion, and degradation. These processes are tightly controlled through intricate networks of positive and negative feedback loops, which shape the gradient and enhance its reproducibility between individual embryos and developmental contexts. In the past three decades, many of the components comprising the morphogen signaling cascades have been identified and sorted into pathways, enabling one to start addressing seminal questions regarding their functionality: How is it that morphogen signaling is reproducible from one embryo to the next, despite fluctuations in the levels of signaling components, temperature differences, variations in size, or unequal distribution of components between daughter cells? Are there underlying mechanisms that assure a reproducible response? Are these mechanisms conserved across species, similar to the signaling pathways they control?In this review, we outline insights we gained by quantitatively analyzing the process of morphogen gradient formation. We focus on mechanisms that buffer morphogen profiles against fluctuations in gene dosage, and describe general means by which such buffering is enhanced. These mechanisms include self-enhanced morphogen degradation and pre-steady-state decoding. In addition, we describe a more specific “shuttling” mechanism that is used to generate a sharp and robust profile of a morphogen activity from a source that is broadly produced. We discuss the implication of the shuttling mechanism for the ability of embryos to adjust their pattern with size. Finally, we consider the transformation of the smooth gradient profile into sharp borders of gene expression in the signal-receiving cells.     

Forming and Interpreting Gradients in the Early Xenopus Embryo

The amphibian embryo provides a powerful model system to study morphogen gradients because of the ease with which it is possible to manipulate the early embryo. In particular, it is possible to introduce exogenous sources of morphogen, to follow the progression of the signal, to monitor the cellular response to induction, and to up- or down-regulate molecules that are involved in all aspects of long-range signaling. In this article, I discuss the evidence that gradients exist in the early amphibian embryo, the way in which morphogens might traverse a field of cells, and the way in which different concentrations of morphogens might be interpreted to activate the expression of different genes.The idea that a morphogen gradient activates the expression of different genes at different concentrations was perhaps stated most clearly by Wolpert''s French flag model, in which a graded signal activates the expression of “blue,” “white,” and “red” genes at high, intermediate, and low concentrations (Wolpert 1969). Since that original work, great progress has been made in identifying morphogens and their target genes and it is now clear that the spatial pattern of gene expression in the developing embryo is frequently established by graded signals of this sort. But many questions remain, and in particular little is known about how gradients are established in the embryo with the necessary precision and how cells interpret different concentrations of morphogen to activate different genes. I discuss these issues with respect to mesoderm induction in the developing amphibian embryo.     

Nodal Morphogens

Nodal signals belong to the TGF-β superfamily and are essential for the induction of mesoderm and endoderm and the determination of the left–right axis. Nodal signals can act as morphogens—they have concentration-dependent effects and can act at a distance from their source of production. Nodal and its feedback inhibitor Lefty form an activator/inhibitor pair that behaves similarly to postulated reaction–diffusion models of tissue patterning. Nodal morphogen activity is also regulated by microRNAs, convertases, TGF-β signals, coreceptors, and trafficking factors. This article describes how Nodal morphogens pattern embryonic fields and discusses how Nodal morphogen signaling is modulated.In his 1901 book “Regeneration,” Thomas Hunt Morgan speculated that “if we suppose the materials or structures that are characteristic of the vegetative half are gradually distributed from the vegetative to the animal half in decreasing amounts, then any piece of the egg will contain more of these things at one pole than the other” and “gastrulation depends on the relative amounts of the materials in the different parts of the blastula” (Morgan 1901). Although Morgan’s speculations referred to the sea urchin embryo, they foretold our current understanding of morphogen gradients in frog and fish development. Morgan’s “materials,” “structures,” and “things” are the Nodal signals that create a vegetal-to-animal activity gradient to regulate germ layer formation and patterning. This article discusses how Nodal signaling provides positional information to fields of cells. I first portray the components of the signaling pathway and describe the role of Nodal signals in mesendoderm induction and left–right axis specification. I then discuss how Nodal morphogen gradients are thought to be generated, modulated, and interpreted.     

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.     

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.     

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.     

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.     

Morphogen Gradient Formation

How morphogen gradients are formed in target tissues is a key question for understanding the mechanisms of morphological patterning. Here, we review different mechanisms of morphogen gradient formation from theoretical and experimental points of view. First, a simple, comprehensive overview of the underlying biophysical principles of several mechanisms of gradient formation is provided. We then discuss the advantages and limitations of different experimental approaches to gradient formation analysis.How a multicellular organism develops from a single fertilized cell has fascinated people throughout history. By looking at chick embryos of different developmental stages, Aristotle first noted that development is characterized by growing complexity and organization of the embryo (Balme 2002). During the 19th century, two events were recognized as key in development: cell proliferation and differentiation. Driesch first noted that to form organisms with correct morphological pattern and size, these processes must be controlled at the level of the whole organism. When he separated two sea urchin blastomeres, they produced two half-sized blastula, showing that cells are potentially independent, but function together to form a whole organism (Driesch 1891, 1908). Morgan noted the polarity of organisms and that regeneration in worms occurs with different rates at different positions. This led him to postulate that regeneration phenomena are influenced by gradients of “formative substances” (Morgan 1901).The idea that organisms are patterned by gradients of form-providing substances was explored by Boveri and Hörstadius to explain the patterning of the sea urchin embryo (Boveri 1901; Hörstadius 1935). The discovery of the Spemann organizer, i.e., a group of dorsal cells that when grafted onto the opposite ventral pole of a host gastrula induce a secondary body axis (Spemann and Mangold 1924), suggested that morphogenesis results from the action of signals that are released from localized groups of cells (“organizing centers”) to induce the differentiation of the cells around them (De Robertis 2006). Child proposed that these patterning “signals” represent metabolic gradients (Child 1941), but the mechanisms of their formation, regulation, and translation into pattern remained elusive.In 1952, Turing showed that chemical substances, which he called morphogens (to convey the idea of “form producers”), could self-organize into spatial patterns, starting from homogenous distributions (Turing 1952). Turing’s reaction–diffusion model shows that two or more morphogens with slightly different diffusion properties that react by auto- and cross-catalyzing or inhibiting their production, can generate spatial patterns of morphogen concentration. The reaction–diffusion formalism was used to model regeneration in hydra (Turing 1952), pigmentation of fish (Kondo and Asai 1995; Kondo 2002), and snails (Meinhardt 2003).At the same time that Turing showed that pattern can self-organize from the production, diffusion, and reaction of morphogens in all cells, the idea that morphogens are released from localized sources (“organizers” à la Spemann) and form concentration gradients was still explored. This idea was formalized by Wolpert with the French flag model for generation of positional information (Wolpert 1969). According to this model, morphogen is secreted from a group of source cells and forms a gradient of concentration in the target tissue. Different target genes are expressed above distinct concentration thresholds, i.e., at different distances to the source, hence generating a spatial pattern of gene expression (Fig. 1C).Open in a separate windowFigure 1.Tissue geometry and simplifications. (A) Gradients in epithelia (left) and mesenchymal tissues (right). Because of symmetry considerations, one row of cells (red outline) is representative for the whole gradient. (B) Magnified view of the red row of cells shown in A. Cells with differently colored nuclei (brown, orange, and blue) express different target genes. (C) A continuum model in which individual cells are ignored and the concentration is a function of the positions x. The morphogen activates different target genes above different concentration thresholds (brown and orange).Experiments in the 1970s and later confirmed that tissues are patterned by morphogen gradients. Sander showed that a morphogen released from the posterior cytoplasm specifies anterioposterior position in the insect egg (Sander 1976). Chick wing bud development was explained by a morphogen gradient emanating from the zone of polarizing activity to specify digit positions (Saunders 1972; Tickle, et al. 1975; Tickle 1999). The most definitive example of a morphogen was provided with the identification of Bicoid function in the Drosophila embryo (Nüsslein-Volhard and Wieschaus 1980; Frohnhöfer and Nüsslein-Volhard 1986; Nüsslein-Volhard et al. 1987) and the visualization of its gradient by antibody staining (Driever and Nüsslein-Volhard 1988b, 1988a; reviewed in Ephrussi and St Johnston 2004). Since then, many examples of morphogen gradients acting in different organs and species have been found.In an attempt to understand pattern formation in more depth, quantitative models of gradient formation have been developed. An early model by Crick shows that freely diffusing morphogen produced in a source cell and destroyed in a “sink” cell at a distance would produce a linear gradient in developmentally relevant timescales (Crick 1970). Today, it is known that a localized “sink” is not necessary for gradient formation: Gradients can form if all cells act as sinks and degrade morphogen, or even if morphogen is not degraded at all. Here, we review different mechanisms of gradient formation, the properties of these gradients, and the implications for patterning. We discuss the theory behind these mechanisms and the supporting experimental data.     

Morphogen gradients,in theory

The idea that morphogen gradients are established by a process of repeated cycles of exocytosis and endocytosis-so-called planar transcytosis-has been gaining acceptance. This is now challenged by a theoretical approach that experimental biologists should not dismiss; diffusive mechanisms of gradient formation may be correct after all.     

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.     

Theoretical and experimental approaches to understand morphogen gradients

Morphogen gradients, which specify different fates for cells in a direct concentration‐dependent manner, are a highly influential framework in which pattern formation processes in developmental biology can be characterized. A common analysis approach is combining experimental and theoretical strategies, thereby fostering relevant data on the dynamics and transduction of gradients. The mechanisms of morphogen transport and conversion from graded information to binary responses are some of the topics on which these combined strategies have shed light. Herein, we review these data, emphasizing, on the one hand, how theoretical approaches have been helpful and, on the other hand, how these have been combined with experimental strategies. In addition, we discuss those cases in which gradient formation and gradient interpretation at the molecular and/or cellular level may influence each other within a mutual feedback loop. To understand this interplay and the features it yields, it becomes essential to take system‐level approaches that combine experimental and theoretical strategies.     

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.     

Novel brain wiring functions for classical morphogens: a role as graded positional cues in axon guidance

During embryonic development, morphogens act as graded positional cues to dictate cell fate specification and tissue patterning. Recent findings indicate that morphogen gradients also serve to guide axonal pathfinding during development of the nervous system. These findings challenge our previous notions about morphogens and axon guidance molecules, and suggest that these proteins, rather than having sharply divergent functions, act more globally to provide graded positional information that can be interpreted by responding cells either to specify cell fate or to direct axonal pathfinding. This review presents the roles identified for members of three prominent morphogen families--the Hedgehog, Wnt and TGFbeta/BMP families--in axon guidance, and discusses potential implications for the molecular mechanisms underlying their guidance functions.     

Models for cell differentiation and generation of polarity in diffusion-governed morphogenetic fields

Models based on molecular mechanisms are presented for pattern formation in developing organisms. It is assumed that there exists a diffusion governed gradient in the morphogenetic field. It is shown that cellular differentiation and the subsequent pattern formation result from the interaction of the diffusing morphogen with the genetic regulatory mechanism of cells. In a second stage it is shown that starting from a homogeneous distribution of morphogen, polarity can be generated spontaneously in the morphogenetic field giving rise to the establishment of a gradient. The stability of these gradients is demonstrated. The onset of a morphogenetic gradient and pattern formation are combined in a single coherent model. Size invariance and its biological implications are discussed.     

Measurement and perturbation of morphogen lifetime: effects on gradient shape

Protein lifetime is of critical importance for most biological processes and plays a central role in cell signaling and embryonic development, where it impacts the absolute concentration of signaling molecules and, potentially, the shape of morphogen gradients. Early conceptual and mathematical models of gradient formation proposed that steady-state gradients are established by an equilibration between the lifetime of a morphogen and its rates of synthesis and diffusion, though whether gradients in fact reach steady state before being read out is a matter of controversy. In any case, this class of models predicts that protein lifetime is a key determinant of both the time to steady state and the spatial extent of a gradient. Using a method that employs repeated photoswitching of a fusion of the morphogen Bicoid (Bcd) and the photoconvertible fluorescent protein Dronpa, we measure and modify the lifetime of Dronpa-Bcd in living Drosophila embryos. We find that the lifetime of Bcd is dynamic, changing from 50 min before mitotic cycle 14 to 15 min during cellularization. Moreover, by measuring total quantities of Bcd over time, we find that the gradient does not reach steady state. Finally, using a nearly continuous low-level conversion to the dark state of Dronpa-Bcd to mimic the effect of increased degradation, we demonstrate that perturbation of protein lifetime changes the characteristic length of the gradient, providing direct support for a mechanism based on synthesis, diffusion, and degradation.     

Self-organized shuttling: generating sharp dorsoventral polarity in the early Drosophila embryo

Morphogen gradients pattern tissues and organs during development. When morphogen production is spatially restricted, diffusion and degradation are sufficient to generate sharp concentration gradients. It is less clear how sharp gradients can arise within the source of a broadly expressed morphogen. A recent solution relies on localized production of an inhibitor outside the domain of morphogen production, which effectively redistributes (shuttles) and concentrates the morphogen within its expression domain. Here, we study how a sharp gradient is established without a localized inhibitor, focusing on early dorsoventral patterning of the Drosophila embryo, where an active ligand and its inhibitor are concomitantly generated in a broad ventral domain. Using theory and experiments, we show that?a sharp?Toll activation gradient is produced through "self-organized shuttling," which dynamically relocalizes inhibitor production to lateral regions, followed by inhibitor-dependent ventral shuttling of the activating ligand Sp?tzle. Shuttling may represent?a general paradigm for patterning early embryos. PAPERFLICK: