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.     

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.     

Mutual repression enhances the steepness and precision of gene expression boundaries

Embryonic development is driven by spatial patterns of gene expression that determine the fate of each cell in the embryo. While gene expression is often highly erratic, embryonic development is usually exceedingly precise. In particular, gene expression boundaries are robust not only against intra-embryonic fluctuations such as noise in gene expression and protein diffusion, but also against embryo-to-embryo variations in the morphogen gradients, which provide positional information to the differentiating cells. How development is robust against intra- and inter-embryonic variations is not understood. A common motif in the gene regulation networks that control embryonic development is mutual repression between pairs of genes. To assess the role of mutual repression in the robust formation of gene expression patterns, we have performed large-scale stochastic simulations of a minimal model of two mutually repressing gap genes in Drosophila, hunchback (hb) and knirps (kni). Our model includes not only mutual repression between hb and kni, but also the stochastic and cooperative activation of hb by the anterior morphogen Bicoid (Bcd) and of kni by the posterior morphogen Caudal (Cad), as well as the diffusion of Hb and Kni between neighboring nuclei. Our analysis reveals that mutual repression can markedly increase the steepness and precision of the gap gene expression boundaries. In contrast to other mechanisms such as spatial averaging and cooperative gene activation, mutual repression thus allows for gene-expression boundaries that are both steep and precise. Moreover, mutual repression dramatically enhances their robustness against embryo-to-embryo variations in the morphogen levels. Finally, our simulations reveal that diffusion of the gap proteins plays a critical role not only in reducing the width of the gap gene expression boundaries via the mechanism of spatial averaging, but also in repairing patterning errors that could arise because of the bistability induced by mutual repression.     

Elucidating multi-input processing 3-node gene regulatory network topologies capable of generating striped gene expression patterns

A central problem in developmental and synthetic biology is understanding the mechanisms by which cells in a tissue or a Petri dish process external cues and transform such information into a coherent response, e.g., a terminal differentiation state. It was long believed that this type of positional information could be entirely attributed to a gradient of concentration of a specific signaling molecule (i.e., a morphogen). However, advances in experimental methodologies and computer modeling have demonstrated the crucial role of the dynamics of a cell’s gene regulatory network (GRN) in decoding the information carried by the morphogen, which is eventually translated into a spatial pattern. This morphogen interpretation mechanism has gained much attention in systems biology as a tractable system to investigate the emergent properties of complex genotype-phenotype maps. In this study, we apply a Markov chain Monte Carlo (MCMC)-like algorithm to probe the design space of three-node GRNs with the ability to generate a band-like expression pattern (target phenotype) in the middle of an arrangement of 30 cells, which resemble a simple (1-D) morphogenetic field in a developing embryo. Unlike most modeling studies published so far, here we explore the space of GRN topologies with nodes having the potential to perceive the same input signal differently. This allows for a lot more flexibility during the search space process, and thus enables us to identify a larger set of potentially interesting and realizable morphogen interpretation mechanisms. Out of 2061 GRNs selected using the search space algorithm, we found 714 classes of network topologies that could correctly interpret the morphogen. Notably, the main network motif that generated the target phenotype in response to the input signal was the type 3 Incoherent Feed-Forward Loop (I3-FFL), which agrees with previous theoretical expectations and experimental observations. Particularly, compared to a previously reported pattern forming GRN topologies, we have uncovered a great variety of novel network designs, some of which might be worth inquiring through synthetic biology methodologies to test for the ability of network design with minimal regulatory complexity to interpret a developmental cue robustly.     

A model of gradient interpretation based on morphogen binding

We propose a model in which pattern formation is controlled by several concentration gradients of “morphogens” and by allosteric proteins which bind them. In this model, each protein can bind up to two molecules of each morphogen and has an “active state” when one molecule of each morphogen is bound. The concentration of the active state of such a “morphogen binding protein” varies with position in a way that depends on the values given the binding constants. In a contour map of the active state concentration, the contours can have a variety of simple shapes.Simply-shaped regions of cell differentiation can be defined directly by concentration contours of a morphogen binding protein using a threshold-sensing mechanism. More complex shapes may be generated using several proteins and a “winner-take-all” rule according to which each protein specifies some particular sort of cell differentiation and the differentiation of cells in any position is governed by the protein with the highest active state concentration.We present an application of our model to the vertebrate limb skeleton; we use the “winner-take-all” mechanism and thirteen morphogen binding proteins, eleven of which specify cartilage formation. In this model we use one morphogen binding protein to specify the shaft of a typical long bone and one for each epiphysis. Our model is reasonably successful in imitating the in vivo positions and orientations of developing bones and in generating simple, plausible-looking articular surfaces.In addition to the morphogen-binding model we propose a mechanism which could transform morphogen-binding patterns into high-amplitude patterns capable of controlling the activity of structural genes. This “amplifying mechanism” can account for two previously unexplained features of limb skeletal development: the early formation of the diffusely-bounded “scleroblastema” in the limb bud and the center-to-edge gradations in cartilage formation rate which are later seen within individual chondrification foci.A simple modification of the morphogen-binding model provides an explanation for the general anatomical phenomenon of metamerism: The model can account for the formation of inexactly repeating patterns (such as the pattern of the vertebral column) and suggests a mechanism by which such patterns could (1) evolve from exactly repeating patterns, and (2) acquire, in further evolution, a high degree of specialization of the individual repeating units.The most promising approach for testing the morphogen-binding model would appear to involve experiments in which cytoplasm is transferred between cells at various stages of pattern development. Support for the model could also come from the discovery of certain kinds of hereditary limb defects.     

Positional information and patterning revisited

The concept of positional information proposes that cells acquire positional values as in a coordinate system, which they interpret by developing in particular ways to give rise to spatial patterns. Some of the best evidence for positional information comes from regeneration experiments, and the patterning of the leg and antenna in Drosophila and the vertebrate limb. Central problems are how positional information is set up, how it is recorded, and then how it is interpreted by the cells. A number of models have been proposed for the setting up of positional gradients, and most are based on diffusion of a morphogen and its interactions with extracellular molecules. It is argued that diffusion may not be reliable mechanism. There are also mechanisms based on timing. There is no good evidence for the quantitative aspects of any of the gradients and details how they are set up. The way in which a signalling gradient regulates differential gene expression in a concentration-dependent manner also raises several mechanistic issues.     

Position matters: variability in the spatial pattern of BMP modulators generates functional diversity

Bone morphogenetic proteins (BMPs) perform a variety of functions during development. Considering a single BMP, what enables its multiple roles in tissues of varied sizes and shapes? What regulates the spatial distribution and activity patterns of the BMP in these different developmental contexts? Some BMP functions require controlling spread of the BMP morphogen, while others require formation of localized, high concentration peaks of BMP activity. Here we review work in Drosophila that describes spatial regulation of the BMP encoded by decapentaplegic (dpp) indifferent developmental contexts. We concentrate on extracellular modulation of BMP function and discuss the mechanisms that generate concentrated peaks of Dpp activity, subdivide territories of different activity levels or regulate spread of the Dpp morphogen from a point source. We compare these findings with data from vertebrates and non‐model organisms to discuss how changes in the regulation of Dpp distribution by extracellular modulators may lead to variability in dpp function in different species. genesis 49:698–718, 2011. © 2011 Wiley‐Liss, Inc.     

Temporal and spatial differentiation in seedling emergence may promote species coexistence in Mediterranean fire‐prone ecosystems

Mediterranean ecosystems are hotspots of species richness where fire is one of the key processes influencing their structure, composition and function. Post‐fire seedling emergence constitutes a crucial event in the life cycle of plants and species‐specific temporal and spatial patterns of seedling emergence have been hypothesized to contribute to the high diversity in these ecosystems. Here we study the temporal and spatial patterns of seedling emergence observed for the four dominant species (Cistus albidus, Ulex parviflorus, Helianthemum marifolium, Ononis fruticosa) after an experimental fire in a Mediterranean gorse shrubland. In a first analysis we compared the timing of emergence of each species using the Kaplan‐Meier method. The spatial component of seedling emergence and the spatiotemporal relationship between different cohorts of the same species were analyzed using recent techniques of spatial point pattern analyses. We found a bimodal temporal pattern of emergence. Emergence of Cistaceae species (H. marifolium and C. albidus) occurred predominantly early after the fire while Fabaceae (O. fruticosa and U. parviflorus) emerged mainly during the following autumn. Individually, all species showed an aggregated spatial pattern and, when testing for pair interactions, we found that the clusters of individual species were spatially segregated. Additionally, the clusters of individual species showed an internal spatial structure where seedlings of different cohorts were spatially segregated. Theoretical models predict that these patterns will promote species coexistence. We identified a number of mechanisms that all have the potential to contribute to the observed pattern formation. However, the potential interaction among these mechanisms are complex and not easy to predict. Our analyses take a significant step forward in studying seedling emergence in fire prone ecosystems since, to our knowledge, this is the first time that both spatial and temporal patterns of all dominant species have been studied together.     

Different designs of kinase-phosphatase interactions and phosphatase sequestration shapes the robustness and signal flow in the MAPK cascade

Background

In developmental biology, there has been a recent focus on the robustness of morphogen gradients as possible providers of positional information. It was shown that functional morphogen gradients present strong biophysical constraints and lack of robustness to noise. Here we explore how the details of the mechanism which underlies the generation of a morphogen gradient can influence those properties.

Results

We contrast three gradient-generating mechanisms, (i) a source-decay mechanism; and (ii) a unidirectional transport mechanism; and (iii) a so-called reflux-loop mechanism. Focusing on the dynamics of the phytohormone auxin in the root, we show that only the reflux-loop mechanism can generate a gradient that would be adequate to supply functional positional information for the Arabidopsis root, for biophysically reasonable kinetic parameters.

Conclusions

We argue that traits that differ in spatial and temporal time-scales can impose complex selective pressures on the mechanism of morphogen gradient formation used for the development of the particular organism.     

Generation model of positional values as cell operation during the development of multicellular organisms

Many conventional models have used the positional information hypothesis to explain each elementary process of morphogenesis during the development of multicellular organisms. Their models assume that the steady concentration patterns of morphogens formed in an extracellular environment have an important property of positional information, so-called “robustness”. However, recent experiments reported that a steady morphogen pattern, the concentration gradient of the Bicoid protein, during early Drosophila embryonic development is not robust for embryo-to-embryo variability. These reports encourage a reconsideration of a long-standing problem in systematic cell differentiation: what is the entity of positional information for cells? And, what is the origin of the robust boundary of gene expression? To address these problems at a cellular level, in this article we pay attention to the re-generative phenomena that show another important property of positional information, “size invariance”. In view of regenerative phenomena, we propose a new mathematical model to describe the generation mechanism of a spatial pattern of positional values. In this model, the positional values are defined as the values into which differentiable cells transform a spatial pattern providing positional information. The model is mathematically described as an associative algebra composed of various terms, each of which is the multiplication of some fundamental operators under the assumption that the operators are derived from the remarkable properties of cell differentiation on an amputation surface in regenerative phenomena. We apply this model to the concentration pattern of the Bicoid protein during the anterior-posterior axis formation in Drosophila, and consider the conditions needed to establish the robust boundary of the expression of the hunchback gene.     

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.     

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.     

Intrinsic and extrinsic regulators of developmental timing: from miRNAs to nutritional cues

A fundamental challenge in biology is to understand the reproducibility of developmental programs between individuals of the same metazoan species. This developmental precision reflects the meticulous integration of temporal control mechanisms with those that specify other aspects of pattern formation, such as spatial and sexual information. The cues that guide these developmental events are largely intrinsic to the organism but can also include extrinsic inputs, such as nutrition or temperature. This review discusses the well-characterized developmental timing mechanism that patterns the C. elegans epidermis. Components of this pathway are conserved, and their links to developmental time control in other species are considered, including the temporal patterning of the fly nervous system. Particular attention is given to the roles of miRNAs in developmental timing and to the emerging mechanisms that link developmental programs to nutritional cues.     

The genetics of phenotypic plasticity. XII. Temporal and spatial heterogeneity

To understand empirical patterns of phenotypic plasticity, we need to explore the complexities of environmental heterogeneity and how it interacts with cue reliability. I consider both temporal and spatial variation separately and in combination, the timing of temporal variation relative to development, the timing of movement relative to selection, and two different patterns of movement: stepping‐stone and island. Among‐generation temporal heterogeneity favors plasticity, while within‐generation heterogeneity can result in cue unreliability. In general, spatial variation more strongly favors plasticity than temporal variation, and island migration more strongly favors plasticity than stepping‐stone migration. Negative correlations among environments between the time of development and selection can result in seemingly maladaptive reaction norms. The effects of higher dispersal rates depend on the life history stage when dispersal occurs and the pattern of environmental heterogeneity. Thus, patterns of environmental heterogeneity can be complex and can interact in unforeseen ways to affect cue reliability. Proper interpretation of patterns of trait plasticity requires consideration of the ecology and biology of the organism. More information on actual cue reliability and the ecological and developmental context of trait plasticity is needed.     

Butterfly Eyespot Patterns: Evidence for Specification by a Morphogen Diffusion Gradient

In this paper we describe a test for Nijhout's (1978, 1980a) hypothesis that the eyespot patterns on butterfly wings are the result of a threshold reaction of the epidermal cells to a concentration gradient of a diffusing degradable morphogen produced by focal cells at the centre of the future eyespot. The wings of the nymphalid butterfly, Bicyclus anynana, have a series of eyespots, each composed of a white pupil, a black disc and a gold outer ring. In earlier extirpation and transplantation experiments (Nijhout 1980a; French and Brakefield, 1995) it has been established that these eyespots are indeed organised around groups of signalling cells active during the first hours of pupal development. If these cells were to supply the positional information for eyespot formation in accordance with Nijhout's diffusion-degradation gradient model, then, when two foci are close together, the signals should sum, and this effect should be apparent in the detailed shape of the resulting pigment pattern. We give an equation for the form of the contours that would be obtained in this manner. We use this to test the morphogen gradient hypothesis on measurements of the outlines of fused eyespots obtained either by grafting focal cells close together, or by using a mutation (Spotty) that produces adjacent fused eyespots. The contours of the fused patterns were found to satisfy our equation, thus corroborating Nijhout's hypothesis to the extent possible with this particular type of experiment.     

Travelling gradients in interacting morphogen systems

Morphogen gradients are well known to play several important roles in development; however the mechanisms underlying the formation and maintenance of these gradients are often not well understood. In this work, we investigate whether the presence of a secondary morphogen can increase the robustness of the primary morphogen gradient to perturbation, thereby providing a more stable mechanism for development. We base our model around the interactions of Fibroblast Growth Factor 8 and retinoic acid, which have been shown to act as morphogens in many developmental systems. In particular, we investigate the formation of opposing gradients of these morphogens along the antero-posterior axis of vertebrate embryos, thereby controlling temporal and spatial aspects of axis segmentation and neuronal differentiation.     

Developmental mechanisms of longitudinal stripes in the Japanese four‐lined snake

The developmental mechanisms of color patterns formation and its evolution remain unclear in reptilian sauropsids. We, therefore, studied the pigment cell mechanisms of stripe pattern formation during embryonic development of the snake Elaphe quadrivirgata. We identified 10 post‐ovipositional embryonic developmental stages based on external morphological characteristics. Examination for the temporal changes in differentiation, distribution, and density of pigment cells during embryonic development revealed that melanophores first appeared in myotome and body cavity but not in skin surface at Stage 5. Epidermal melanophores were first recognized at Stage 7, and dermal melanophores and iridophores appeared in Stage 9. Stripe pattern first appeared to establish at Stage 8 as a spatial density gradient of epidermal melanophores between the regions of future dark brown longitudinal stripes and light colored background. Our study, thus, provides a comprehensive pigment‐cell‐based understanding of stripe pattern formation during embryonic development. We briefly discuss the importance of the gene expression studies by considering the biologically relevant theoretical models with standard developmental staging for understanding reptilian color pattern evolution.