Dynamic interpretation of hedgehog signaling in the Drosophila wing disc

Dynamics of BMP signaling and stable gene expression in the early Drosophila embryo

In developing tissues, morphogen gradients are thought to initialize gene expression patterns. However, the relationship between the dynamics of morphogen-encoded signals and gene expression decisions is largely unknown. Here we examine the dynamics of the Bone Morphogenetic Protein (BMP) pathway in Drosophila blastoderm-stage embryos. In this tissue, the BMP pathway is highly dynamic: it begins as a broad and weak signal on the dorsal half of the embryo, then 20-30 min later refines into a narrow, intense peak centered on the dorsal midline. This dynamical progression of the BMP signal raises questions of how it stably activates target genes. Therefore, we performed live imaging of the BMP signal and found that dorsal-lateral cells experience only a short transient in BMP signaling, after which the signal is lost completely. Moreover, we measured the transcriptional response of the BMP target gene pannier in live embryos and found it to remain activated in dorsal-lateral cells, even after the BMP signal is lost. Our findings may suggest that the BMP pathway activates a memory, or 'ratchet' mechanism that may sustain gene expression.

Dual-role regulator of a novel miR-3040 in photoperiod-mediated wing dimorphism and wing development in green peach aphid

Wing dimorphism is regarded as an important phenotypic plasticity involved in the migration and reproduction of aphids. However, the signal transduction and regulatory mechanism of wing dimorphism in aphids are still unclear. Herein, the optimal environmental conditions were first explored for inducing winged offspring of green peach aphid, and the short photoperiod was the most important environmental cue to regulate wing dimorphism. Compared to 16 L:8 D photoperiod, the proportion of winged offspring increased to 90% under 8 L:16 D photoperiod. Subsequently, 5 differentially expressed microRNAs (miRNAs) in aphids treated with long and short photoperiods were identified using small RNA sequencing, and a novel miR-3040 was identified as a vital miRNA involved in photoperiod-mediated wing dimorphism. More specifically, the inhibition of miR-3040 expression could reduce the proportion of winged offspring induced by short photoperiod, whereas its activation increased the proportion of winged offspring under long photoperiod. Meanwhile, the expression level of miR-3040 in winged aphids was about 2.5 times that of wingless aphids, and the activation or inhibition of miR-3040 expression could cause wing deformity, revealing the dual-role regulator of miR-3040 in wing dimorphism and wing development. In summary, the current study identified the key environmental cue for wing dimorphism in green peach aphid, and the first to demonstrate the dual-role regulator of miR-3040 in photoperiod-mediated wing dimorphism and wing development.

Hedgehog is relayed through dynamic heparan sulfate interactions to shape its gradient

Cellular differentiation is directly determined by concentration gradients of morphogens. As a central model for gradient formation during development, Hedgehog (Hh) morphogens spread away from their source to direct growth and pattern formation in Drosophila wing and eye discs. What is not known is how extracellular Hh spread is achieved and how it translates into precise gradients. Here we show that two separate binding areas located on opposite sides of the Hh molecule can interact directly and simultaneously with two heparan sulfate (HS) chains to temporarily cross-link the chains. Mutated Hh lacking one fully functional binding site still binds HS but shows reduced HS cross-linking. This, in turn, impairs Hhs ability to switch between both chains in vitro and results in striking Hh gradient hypomorphs in vivo. The speed and propensity of direct Hh switching between HS therefore shapes the Hh gradient, revealing a scalable design principle in morphogen-patterned tissues.

Thermodynamic Modelling of Transcriptional Control: A Sensitivity Analysis

Modelling is a tool used to decipher the biochemical mechanisms involved in transcriptional control. Experimental evidence in genetics is usually supported by theoretical models in order to evaluate the effects of all the possible interactions that can occur in these complicated processes. Models derived from the thermodynamic method are critical in this labour because they are able to take into account multiple mechanisms operating simultaneously at the molecular micro-scale and relate them to transcriptional initiation at the tissular macro-scale. This work is devoted to adapting computational techniques to this context in order to theoretically evaluate the role played by several biochemical mechanisms. The interest of this theoretical analysis relies on the fact that it can be contrasted against those biological experiments where the response to perturbations in the transcriptional machinery environment is evaluated in terms of genetically activated/repressed regions. The theoretical reproduction of these experiments leads to a sensitivity analysis whose results are expressed in terms of the elasticity of a threshold function determining those activated/repressed regions. The study of this elasticity function in thermodynamic models already proposed in the literature reveals that certain modelling approaches can alter the balance between the biochemical mechanisms considered, and this can cause false/misleading outcomes. The reevaluation of classical thermodynamic models gives us a more accurate and complete picture of the interactions involved in gene regulation and transcriptional control, which enables more specific predictions. This sensitivity approach provides a definite advantage in the interpretation of a wide range of genetic experimental results.

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.

Temporal analysis of microRNAs associated with wing development in the English grain aphid, Sitobion avenae (F.) (Homoptera: Aphidiae)

Molecular mechanisms underlying wing evolution and development have been a point of scientific inquiry for decades. Phloem-feeding aphids are one of the most devastating global insect pests, where dispersal of winged morphs lead to annual movements, migrations, and range expansions. Aphids show a polyphenic wing dimorphism trait, and offer a model to study the role of environment in determining morphological plasticity of a single genotype. Despite recent progresses in the genetic understanding of wing polyphenism, the influence of environmental cues remains unclear. To investigate the involvement of miRNAs in wing development, we sequenced small RNA libraries of the English grain aphid, Sitobion avenae (F.) across six different developmental stages. As a result, we identified 113 conserved and 193 S. avenae-specific miRNAs. Gene Ontology and KEGG pathway analyses of putative target mRNAs for the six differentially expressed miRNAs are enriched for wing development processes. Dietary uptake of miR-263a, miR-316, and miR-184a agomirs and antagomirs led to significantly higher mortality (>70%) and a lower proportion of winged morphs (<5%). On the other hand, wing malformation was observed in miR-2 and miR-306 agomirs and miR-2 and miR-14 antagomirs, respectively, suggesting their involvement in S. avenae wing morphogenesis. These combined results not only shed light on the regulatory role of miRNAs in wing dimorphism, but also provide potential novel targets for the long-term sustainable management of S. avenae, a devastating global grain pest.

Cost-precision trade-off relation determines the optimal morphogen gradient for accurate biological pattern formation

Spatial boundaries formed during animal development originate from the pre-patterning of tissues by signaling molecules, called morphogens. The accuracy of boundary location is limited by the fluctuations of morphogen concentration that thresholds the expression level of target gene. Producing more morphogen molecules, which gives rise to smaller relative fluctuations, would better serve to shape more precise target boundaries; however, it incurs more thermodynamic cost. In the classical diffusion-depletion model of morphogen profile formation, the morphogen molecules synthesized from a local source display an exponentially decaying concentration profile with a characteristic length λ. Our theory suggests that in order to attain a precise profile with the minimal cost, λ should be roughly half the distance to the target boundary position from the source. Remarkably, we find that the profiles of morphogens that pattern the Drosophila embryo and wing imaginal disk are formed with nearly optimal λ. Our finding underscores the cost-effectiveness of precise morphogen profile formation in Drosophila development.

Improving the understanding of cytoneme-mediated morphogen gradients by in silico modeling

Morphogen gradients are crucial for the development of organisms. The biochemical properties of many morphogens prevent their extracellular free diffusion, indicating the need of an active mechanism for transport. The involvement of filopodial structures (cytonemes) has been proposed for morphogen signaling. Here, we describe an in silico model based on the main general features of cytoneme-meditated gradient formation and its implementation into Cytomorph, an open software tool. We have tested the spatial and temporal adaptability of our model quantifying Hedgehog (Hh) gradient formation in two Drosophila tissues. Cytomorph is able to reproduce the gradient and explain the different scaling between the two epithelia. After experimental validation, we studied the predicted impact of a range of features such as length, size, density, dynamics and contact behavior of cytonemes on Hh morphogen distribution. Our results illustrate Cytomorph as an adaptive tool to test different morphogen gradients and to generate hypotheses that are difficult to study experimentally.

Graded distribution of signaling molecules (morphogens) is crucial for the development of organisms. Signaling membrane protrusions, called Cytonemes, have been experimentally demonstrated to be involved in morphogen transport and reception. Here, we have developed an in silico model for gradient formation based on key features of cytoneme mediated signaling. We have also implemented the model into an open software tool we named Cytomorph, and validated it by comparing its simulations with experimental data obtained from Hedgehog morphogen distribution. Finally, we have generated in silico predictions for the impact of different cytoneme features such as length, size, density, dynamics and contact behavior. Our results show that Cytomorph is an adaptive tool that can facilitate the study of other cytoneme-dependent morphogen gradients, besides being able to generate hypotheses about aspects that remain elusive to experimental approaches.

A mathematical model of the role of aggregation in sonic hedgehog signalling

Effective regulation of the sonic hedgehog (Shh) signalling pathway is essential for normal development in a wide variety of species. Correct Shh signalling requires the formation of Shh aggregates on the surface of producing cells. Shh aggregates subsequently diffuse away and are recognised in receiving cells located elsewhere in the developing embryo. Various mechanisms have been postulated regarding how these aggregates form and what their precise role is in the overall signalling process. To understand the role of these mechanisms in the overall signalling process, we formulate and analyse a mathematical model of Shh aggregation using nonlinear ordinary differential equations. We consider Shh aggregate formation to comprise of multimerisation, association with heparan sulfate proteoglycans (HSPG) and binding with lipoproteins. We show that the size distribution of the Shh aggregates formed on the producing cell surface resembles an exponential distribution, a result in agreement with experimental data. A detailed sensitivity analysis of our model reveals that this exponential distribution is robust to parameter changes, and subsequently, also to variations in the processes by which Shh is recruited by HSPGs and lipoproteins. The work demonstrates the time taken for different sized Shh aggregates to form and the important role this likely plays in Shh diffusion.

The sonic hedgehog (Shh) pathway is vital for normal development in a wide variety of species and its activity is strictly regulated to ensure correct spatiotemporal patterning of numerous developing tissues. Shh signalling requires the formation of Shh aggregates, formed on producing cells via a range of different mechanisms, that then diffuse to receiving cells. We formulate and analyse a mathematical model of the most well described mechanisms, namely monomer multimerisation, and recruitment of Shh by heparan sulfate proteoglycans and lipoproteins. Our results illustrate a distribution of the size and quantities of aggregates formed by these mechanisms. We found that as a consequence of competition between the mechanisms for Shh monomers the shape distribution of Shh aggregates resembles an exponential distribution. We also found the distribution to be robust to both parameter changes and variations to the processes by which mechanisms recruit Shh. We report that our approach and subsequent results demonstrate that these mechanisms act in synergy allowing Shh to aggregate in various quantities with diverse diffusive abilities. We postulate that this regulation contributes significantly to aid precision in signalling for Shh in areas of development.

Dynamic patterning by morphogens illuminated by cis-regulatory studies

Morphogen concentration changes in space as well as over time during development. However, how these dynamics are interpreted by cells to specify fate is not well understood. Here, we focus on two morphogens: the maternal transcription factors Bicoid and Dorsal, which directly regulate target genes to pattern Drosophila embryos. The actions of these factors at enhancers has been thoroughly dissected and provides a rich platform for understanding direct input by morphogens and their changing roles over time. Importantly, Bicoid and Dorsal do not work alone; we also discuss additional inputs that work with morphogens to control spatiotemporal gene expression in embryos.

Scaling a Dpp Morphogen Gradient through Feedback Control of Receptors and Co-receptors

Gradients of decapentaplegic (Dpp) pattern Drosophila wing imaginal discs, establishing gene expression boundaries at specific locations. As discs grow, Dpp gradients expand, keeping relative boundary positions approximately stationary. Such scaling fails in mutants for Pentagone (pent), a gene repressed by Dpp that encodes a diffusible protein that expands Dpp gradients. Although these properties fit a recent mathematical model of automatic gradient scaling, that model requires an expander that spreads with minimal loss throughout a morphogen field. Here, we show that Pent's actions are confined to within just a few cell diameters of its site of synthesis and can be phenocopied by manipulating non-diffusible Pent targets strictly within the Pent expression domain. Using genetics and mathematical modeling, we develop an alternative model of scaling driven by feedback downregulation of Dpp receptors and co-receptors. Among the model's predictions is a size beyond which scaling fails-something we observe directly in wing discs.

Temporal flexibility of gene regulatory network underlies a novel wing pattern in flies

Developmental genes can be coopted to generate evolutionary novelties by changing their spatial regulation. However, developmental genes seldom act independently, but rather work in a gene regulatory network (GRN). How is it possible to recruit a single gene from a whole GRN? What are the properties that allow parallel cooptions of the same genes during evolution? Here, we show that a novel engrailed gene expression underlies a novel wing color pattern in flies. We show that cooption is facilitated 1) because of GRN flexibility over development and 2) because every single gene of the GRN has its own functional time window. We suggest these two temporal properties could explain why the same gene can be independently recruited several times during evolution.

Organisms have evolved endless morphological, physiological, and behavioral novel traits during the course of evolution. Novel traits were proposed to evolve mainly by orchestration of preexisting genes. Over the past two decades, biologists have shown that cooption of gene regulatory networks (GRNs) indeed underlies numerous evolutionary novelties. However, very little is known about the actual GRN properties that allow such redeployment. Here we have investigated the generation and evolution of the complex wing pattern of the fly Samoaia leonensis. We show that the transcription factor Engrailed is recruited independently from the other players of the anterior–posterior specification network to generate a new wing pattern. We argue that partial cooption is made possible because 1) the anterior–posterior specification GRN is flexible over time in the developing wing and 2) this flexibility results from the fact that every single gene of the GRN possesses its own functional time window. We propose that the temporal flexibility of a GRN is a general prerequisite for its possible cooption during the course of evolution.

Spatiotemporal control of gene expression boundaries using a feedforward loop

BACKGROUND

A feedforward loop (FFL) is commonly observed in several biological networks. The FFL network motif has been mostly studied with respect to variation of the input signal in time, with only a few studies of FFL activity in a spatially distributed system such as morphogen-mediated tissue patterning. However, most morphogen gradients also evolve in time.

RESULTS

We studied the spatiotemporal behavior of a coherent FFL in two contexts: (a) a generic, oscillating morphogen gradient and (b) the dorsal-ventral patterning of the early Drosophila embryo by a gradient of the NF-κB homolog dorsal with its early target Twist. In both models, we found features in the dynamics of the intermediate node-phase difference and noise filtering-that were largely independent of the parameterization of the models, and thus were functions of the structure of the FFL itself. In the dorsal gradient model, we also found that proper target gene expression was not possible without including the effect of maternal pioneer factor Zelda.

CONCLUSIONS

An FFL buffers fluctuation to changes in the morphogen signal ensuring stable gene expression boundaries.

Dynamic Hh signalling can generate temporal information during tissue patterning

The differentiation of tissues and organs requires that cells exchange information in space and time. Spatial information is often conveyed by morphogens: molecules that disperse across receiving cells to generate signalling gradients. Cells translate such concentration gradients into space-dependent patterns of gene expression and cellular behaviour. But could morphogen gradients also convey developmental time? Here, by investigating the developmental role of Hh on a component of the Drosophila visual system, the ocellar retina, we have discovered that ocellar cells use the non-linear gradient of Hh as a temporal cue, collectively performing the biological equivalent of a mathematical logarithmic transformation. In this way, a morphogen diffusing from a non-moving source is decoded as a wave of differentiating photoreceptors that travels at constant speed throughout the retinal epithelium.

The formation of the Thickveins (Tkv) gradient in Drosophila wing discs: A theoretical study

The development of the wing imaginal disc (wing disc) is commonly adopted for the studies of patterning and growth which are two fundamental problems in developmental biology. Decapentaplegic (Dpp) signaling regulates several aspects of wing development, such as the anterior (A)-posterior (P) patterning, cellular growth rate, and cell adhesion. The distribution and activity of Dpp signaling are controlled in part by the expression level of its major type I receptor, Thickveins (Tkv). In this paper, we focus on theoretically investigating mechanisms by which the highly asymmetric pattern of Tkv is established in Drosophila wing discs. To the end, a mathematical model of Hh signaling and Dpp signaling is proposed and validated by comparisons with experimental observations. Our model provides a comprehensive view of the formation of Tkv gradients in wing discs. We found that engrailed (En), Hedgehog (Hh) signaling, and Dpp signaling cooperate to establish the asymmetric gradients of Tkv and pMad in the wing disc. Moreover, our model suggests a Brinker-mediated mechanism of Dpp-dependent repression of Tkv. Based on this mechanism, a couple of predicted experimental observations have been provided for further lab confirmation.

Ventral neural patterning in the absence of a Shh activity gradient from the floorplate

BACKGROUND

Vertebrate spinal cord development requires Sonic Hedgehog (Shh) signaling from the floorplate and notochord, where it is thought to act in concentration dependent manner to pattern distinct cell identities along the ventral-to-dorsal axis. While in vitro experiments demonstrate naïve neural tissues are sensitive to small changes in Shh levels, genetic studies illustrate that some degree of ventral patterning can occur despite significant perturbations in Shh signaling. Consequently, the mechanistic relationship between Shh morphogen levels and acquisition of distinct cell identities remains unclear.

RESULTS

We addressed this using Hedgehog acetyltransferase (Hhat^Creface ) and Wiggable mouse mutants. Hhat encodes a palmitoylase required for the secretion of Hedgehog proteins and formation of the Shh gradient. In its absence, the spinal cord develops without floorplate cells and V3 interneurons. Wiggable is an allele of the Shh receptor Patched1 (Ptch1^Wig ) that is unable to inhibit Shh signal transduction, resulting in expanded ventral progenitor domains. Surprisingly, Hhat^{Creface/Creface} ; Ptch1^Wig/Wig double mutants displayed fully restored ventral patterning despite an absence of Shh secretion from the floorplate.

CONCLUSIONS

The full range of neuronal progenitor types can be generated in the absence of a Shh gradient provided pathway repression is dampened, illustrating the complexity of morphogen dynamics in vertebrate patterning. Developmental Dynamics 247:170-184, 2018. © 2017 Wiley Periodicals, Inc.

Hedgehog signalling is required for cell survival in Drosophila wing pouch cells

An appropriate balance between cell survival and cell death is essential for correct pattern formation in the animal tissues and organs. Previous studies have shown that the short-range signalling molecule Hedgehog (Hh) is required for cell proliferation and pattern formation in the Drosophila central wing discs. Signal transduction by one of the Hh targets, the morphogen Decapentaplegic (Dpp), is required for not only cell proliferation, but also cell survival in the pouch cells. However, Hh function in cell survival and cell death has not been revealed. Here, we found that loss of Hh signal activity induces considerable Caspase-dependent cell death in the wing pouch cells, and this process was independent of both Dpp signalling and Jun-N-terminal kinase (JNK) signalling. Loss of Hh induced activation of the pro-apoptotic gene hid and inhibition of diap1. Therefore, we identified an important role of Hh signalling in cell survival during Drosophila wing development.

Perspectives on Intra- and Intercellular Trafficking of Hedgehog for Tissue Patterning

Intercellular communication is a fundamental process for correct tissue development. The mechanism of this process involves, among other things, the production and secretion of signaling molecules by specialized cell types and the capability of these signals to reach the target cells in order to trigger specific responses. Hedgehog (Hh) is one of the best-studied signaling pathways because of its importance during morphogenesis in many organisms. The Hh protein acts as a morphogen, activating its targets at a distance in a concentration-dependent manner. Post-translational modifications of Hh lead to a molecule covalently bond to two lipid moieties. These lipid modifications confer Hh high affinity to lipidic membranes, and intense studies have been carried out to explain its release into the extracellular matrix. This work reviews Hh molecule maturation, the intracellular recycling needed for its secretion and the proposed carriers to explain Hh transportation to the receiving cells. Special focus is placed on the role of specialized filopodia, also named cytonemes, in morphogen transport and gradient formation.

A Model of the Spatio-temporal Dynamics of Drosophila Eye Disc Development

Patterning and growth are linked during early development and have to be tightly controlled to result in a functional tissue or organ. During the development of the Drosophila eye, this linkage is particularly clear: the growth of the eye primordium mainly results from proliferating cells ahead of the morphogenetic furrow (MF), a moving signaling wave that sweeps across the tissue from the posterior to the anterior side, that induces proliferating cells anterior to it to differentiate and become cell cycle quiescent in its wake. Therefore, final eye disc size depends on the proliferation rate of undifferentiated cells and on the speed with which the MF sweeps across the eye disc. We developed a spatio-temporal model of the growing eye disc based on the regulatory interactions controlled by the signals Decapentaplegic (Dpp), Hedgehog (Hh) and the transcription factor Homothorax (Hth) and explored how the signaling patterns affect the movement of the MF and impact on eye disc growth. We used published and new quantitative data to parameterize the model. In particular, two crucial parameter values, the degradation rate of Hth and the diffusion coefficient of Hh, were measured. The model is able to reproduce the linear movement of the MF and the termination of growth of the primordium. We further show that the model can explain several mutant phenotypes, but fails to reproduce the previously observed scaling of the Dpp gradient in the anterior compartment.

Spatiotemporal analysis of different mechanisms for interpreting morphogen gradients

During development, multicellular organisms must accurately control both temporal and spatial aspects of tissue patterning. This is often achieved using morphogens, signaling molecules that form spatially varying concentrations and so encode positional information. Typical analysis of morphogens assumes that spatial information is decoded in steady state by measuring the value of the morphogen concentration. However, recent experimental work suggests that both pre-steady-state readout and measurement of spatial and temporal derivatives of the morphogen concentration can play important roles in defining boundaries. Here, we undertake a detailed theoretical and numerical study of the accuracy of patterning-both in space and time-in models where readout is provided not by the morphogen concentration but by its spatial and temporal derivatives. In both cases we find that accurate patterning can be achieved, with sometimes even smaller errors than directly reading the morphogen concentration. We further demonstrate that such models provide other potential benefits to the system, such as the ability to switch on and off gene response with a high degree of spatiotemporal accuracy. Finally, we discuss how such derivatives might be calculated biologically and examine these models in relation to Sonic Hedgehog signaling in the vertebrate central nervous system. We show that, when coupled to a downstream transcriptional network, pre-steady-state measurement of the temporal change in the Shh morphogen is a plausible mechanism for determining precise gene boundaries in both space and time.

DYNAMICS OF GLI REGULATION AND A STRATEGY TO CONTROL CANCEROUS SITUATION: HEDGEHOG SIGNALING PATHWAY REVISITED

The hedgehog signaling cascade generates highly diverse, fine-tuned responses in response to the external stimulus by the sonic hedgehog (SHH) protein. This is required for the flawless functioning of the cell, its development, survival and proliferation; maintained through production of Glioma protein (GLI) and transcriptional activation of its target genes. Any change in the behavior of GLI response by ectopic expression of SHH or mutations in the core pathway components may cause serious consequences in the cell fate through rapid, uncontrolled and elevated production of GLI. Here, we present a simple but extensive computational model that considers the detailed reaction mechanisms involved in the hedgehog signal transduction and provides a detailed insight into regulation of GLI. For the first time, by explicit involvement of suppressor of fused (SUFU) and Hedgehog interacting protein (HHIP) reaction kinetics in the model, we try to demonstrate the vital importance of HHIP and SUFU in maintaining the graded response of GLI in response to SHH. By performing parameter variations, we capture the conversion of a graded response of GLI to an ultrasensitive switch under SUFU-deficient conditions that might predispose abnormal embryonic development and the irreversible switching response of GLI that corresponds to signal-independent pathway activation observed in cancers.

Spatiotemporal regulation of GLI target genes in the mammalian limb bud

GLI proteins convert Sonic hedgehog (Shh) signaling into a transcriptional output in a tissue-specific fashion. The Shh pathway has been extensively studied in the limb bud, where it helps regulate growth through a SHH-FGF feedback loop. However, the transcriptional response is still poorly understood. We addressed this by determining the gene expression patterns of approximately 200 candidate GLI-target genes and identified three discrete SHH-responsive expression domains. GLI-target genes expressed in the three domains are predominately regulated by derepression of GLI3 but have different temporal requirements for SHH. The GLI binding regions associated with these genes harbor both distinct and common DNA motifs. Given the potential for interaction between the SHH and FGF pathways, we also measured the response of GLI-target genes to inhibition of FGF signaling and found the majority were either unaffected or upregulated. These results provide the first characterization of the spatiotemporal response of a large group of GLI-target genes and lay the foundation for a systems-level understanding of the gene regulatory networks underlying SHH-mediated limb patterning.

The role of mathematical models in understanding pattern formation in developmental biology

In a Wall Street Journal article published on April 5, 2013, E. O. Wilson attempted to make the case that biologists do not really need to learn any mathematics-whenever they run into difficulty with numerical issues, they can find a technician (aka mathematician) to help them out of their difficulty. He formalizes this in Wilsons Principle No. 1: "It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations." This reflects a complete misunderstanding of the role of mathematics in all sciences throughout history. To Wilson, mathematics is mere number crunching, but as Galileo said long ago, "The laws of Nature are written in the language of mathematics[Formula: see text] the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word." Mathematics has moved beyond the geometry-based model of Galileo's time, and in a rebuttal to Wilson, E. Frenkel has pointed out the role of mathematics in synthesizing the general principles in science (Both point and counter-point are available in Wilson and Frenkel in Notices Am Math Soc 60(7):837-838, 2013). We will take this a step further and show how mathematics has been used to make new and experimentally verified discoveries in developmental biology and how mathematics is essential for understanding a problem that has puzzled experimentalists for decades-that of how organisms can scale in size. Mathematical analysis alone cannot "solve" these problems since the validation lies at the molecular level, but conversely, a growing number of questions in biology cannot be solved without mathematical analysis and modeling. Herein, we discuss a few examples of the productive intercourse between mathematics and biology.

Ptch1 and Gli regulate Shh signalling dynamics via multiple mechanisms

In the vertebrate neural tube, the morphogen Sonic Hedgehog (Shh) establishes a characteristic pattern of gene expression. Here we quantify the Shh gradient in the developing mouse neural tube and show that while the amplitude of the gradient increases over time, the activity of the pathway transcriptional effectors, Gli proteins, initially increases but later decreases. Computational analysis of the pathway suggests three mechanisms that could contribute to this adaptation: transcriptional upregulation of the inhibitory receptor Ptch1, transcriptional downregulation of Gli and the differential stability of active and inactive Gli isoforms. Consistent with this, Gli2 protein expression is downregulated during neural tube patterning and adaptation continues when the pathway is stimulated downstream of Ptch1. Moreover, the Shh-induced upregulation of Gli2 transcription prevents Gli activity levels from adapting in a different cell type, NIH3T3 fibroblasts, despite the upregulation of Ptch1. Multiple mechanisms therefore contribute to the intracellular dynamics of Shh signalling, resulting in different signalling dynamics in different cell types.

Decoding Ci: from partial degradation to inhibition

Hedgehog is a morphogen, which is widely involved in the regulation of cell proliferation, differentiation and tissue patterning during development in both vertebrate and invertebrate, such as in coordination of eye, brain, gonad, gut and tracheal development. In invertebrate, Cubitus interruptus (Ci) modification process is the last identified step before transcriptional activation in the Hh signaling pathway. Ci can form a truncated repressor (Ci(R) /Ci75) or act as an activator (Ci(A) /Ci155) based on Hh gradient to regulate the expressions of target genes. The activity of Ci is mediated by different mechanisms, including processing, trafficking and degradation. While in vertebrate, Glioblastomas (Glis), homologs of Ci, play similar but more complex roles in the regulation of mammals Hh pathway. Hh signaling is responsible for a wide variety of processes during embryonic development and adult tissue homeostasis. Malfunction of Hh signaling could cause various diseases including birth defects and cancers. Enormous efforts were made in the past decades to explore the Hh pathway regulation and the results have provided us important insights into disease diagnosis and therapeutic treatment. In this review, we focus on a small branch of Hh pathway regulation based on studies in the Drosophila system, mainly about Ci degradation, aiming to explain how Ci is modified by different ubiquitin ligases due to the strong or moderate Hh signals and then been subjected to complete or partial degradation by proteasomes. Overall, we intend to offer an overview on how Ci responds to and relays Hh signals in a precise manner to control target genes expressions and ensures proper Hh signal transduction.

An interplay of geometry and signaling enables robust lung branching morphogenesis

Early branching events during lung development are stereotyped. Although key regulatory components have been defined, the branching mechanism remains elusive. We have now used a developmental series of 3D geometric datasets of mouse embryonic lungs as well as time-lapse movies of cultured lungs to obtain physiological geometries and displacement fields. We find that only a ligand-receptor-based Turing model in combination with a particular geometry effect that arises from the distinct expression domains of ligands and receptors successfully predicts the embryonic areas of outgrowth and supports robust branch outgrowth. The geometry effect alone does not support bifurcating outgrowth, while the Turing mechanism alone is not robust to noisy initial conditions. The negative feedback between the individual Turing modules formed by fibroblast growth factor 10 (FGF10) and sonic hedgehog (SHH) enlarges the parameter space for which the embryonic growth field is reproduced. We therefore propose that a signaling mechanism based on FGF10 and SHH directs outgrowth of the lung bud via a ligand-receptor-based Turing mechanism and a geometry effect.

Transcriptional regulation of graded Hedgehog signaling

The Hedgehog (Hh) pathway plays conserved roles in regulating a diverse spectrum of developmental processes. In some developmental contexts, a gradient of Hh protein specifies multiple cell types in a dose-dependent fashion, thereby acting as a morphogen. Hh signaling ultimately acts on the transcriptional level through GLI proteins. In the presence of Hh signaling full length GLI proteins act as transcriptional activators of target genes. Conversely, in the absence of Hh, GLI proteins act as transcriptional repressors. This review will highlight mechanisms contributing to how graded Hh signaling might translate to differential GLI activity and be interpreted into distinct transcriptional responses.

A BMP-FGF morphogen toggle switch drives the ultrasensitive expression of multiple genes in the developing forebrain

Borders are important as they demarcate developing tissue into distinct functional units. A key challenge is the discovery of mechanisms that can convert morphogen gradients into tissue borders. While mechanisms that produce ultrasensitive cellular responses provide a solution, how extracellular morphogens drive such mechanisms remains poorly understood. Here, we show how Bone Morphogenetic Protein (BMP) and Fibroblast Growth Factor (FGF) pathways interact to generate ultrasensitivity and borders in the dorsal telencephalon. BMP and FGF signaling manipulations in explants produced border defects suggestive of cross inhibition within single cells, which was confirmed in dissociated cultures. Using mathematical modeling, we designed experiments that ruled out alternative cross inhibition mechanisms and identified a cross-inhibitory positive feedback (CIPF) mechanism, or "toggle switch", which acts upstream of transcriptional targets in dorsal telencephalic cells. CIPF explained several cellular phenomena important for border formation such as threshold tuning, ultrasensitivity, and hysteresis. CIPF explicitly links graded morphogen signaling in the telencephalon to switch-like cellular responses and has the ability to form multiple borders and scale pattern to size. These benefits may apply to other developmental systems.

A gradient of matrix-bound FGF-2 and perlecan is available to lens epithelial cells

Fibroblast growth factors play a key role in regulating lens epithelial cell proliferation and differentiation via an anteroposterior gradient that exists between the aqueous and vitreous humours. FGF-2 is the most important for lens epithelial cell proliferation and differentiation. It has been proposed that the presentation of FGF-2 to the lens epithelial cells involves the lens capsule as a source of matrix-bound FGF-2. Here we used immunogold labelling to measure the matrix-bound FGF-2 gradient on the inner surface of the lens capsule in flat-mounted preparations to visualize the FGF-2 available to lens epithelial cells. We also correlated FGF-2 levels with levels of its matrix-binding partner perlecan, a heparan sulphate proteoglycan (HSPG) and found the levels of both to be highest at the lens equator. These also coincided with increased levels of phosphorylated extracellular signal-regulated kinase 1 and 2 (pERK1/2) in lens epithelial cells that localised to condensed chromosomes of epithelial cells that were Ki-67 positive. The gradient of matrix-bound FGF-2 (anterior pole: 3.7 ± 1.3 particles/μm²; equator: 8.2 ± 1.9 particles/μm²; posterior pole: 4 ± 0.9 particles/μm²) and perlecan (anterior pole: 2.1 ± 0.4 particles/μm²; equator: 5 ± 2 particles/μm²; posterior pole: 1.9 ± 0.7 particles/μm²) available at the inner lens capsule surface was measured for the bovine lens. These data support the anteroposterior gradient hypothesis and provide the first measurement of the gradient for an important morphogen and its HSPG partner, perlecan, at the epithelial cell-lens capsule interface.

Activation of Smurf E3 ligase promoted by smoothened regulates hedgehog signaling through targeting patched turnover

Hedgehog signaling plays conserved roles in controlling embryonic development; its dysregulation has been implicated in many human diseases including cancers. Hedgehog signaling has an unusual reception system consisting of two transmembrane proteins, Patched receptor and Smoothened signal transducer. Although activation of Smoothened and its downstream signal transduction have been intensively studied, less is known about how Patched receptor is regulated, and particularly how this regulation contributes to appropriate Hedgehog signal transduction. Here we identified a novel role of Smurf E3 ligase in regulating Hedgehog signaling by controlling Patched ubiquitination and turnover. Moreover, we showed that Smurf-mediated Patched ubiquitination depends on Smo activity in wing discs. Mechanistically, we found that Smo interacts with Smurf and promotes it to mediate Patched ubiquitination by targeting the K1261 site in Ptc. The further mathematic modeling analysis reveals that a bidirectional control of activation of Smo involving Smurf and Patched is important for signal-receiving cells to precisely interpret external signals, thereby maintaining Hedgehog signaling reliability. Finally, our data revealed an evolutionarily conserved role of Smurf proteins in controlling Hh signaling by targeting Ptc during development.

Injury-induced BMP signaling negatively regulates Drosophila midgut homeostasis

Injury-induced BMP signaling in the midgut negatively regulates intestinal stem cell division, whereas regional constitutive BMP signaling promotes copper cell differentiation.

Although much is known about injury-induced signals that increase rates of Drosophila melanogaster midgut intestinal stem cell (ISC) proliferation, it is largely unknown how ISC activity returns to quiescence after injury. In this paper, we show that the bone morphogenetic protein (BMP) signaling pathway has dual functions during midgut homeostasis. Constitutive BMP signaling pathway activation in the middle midgut mediated regional specification by promoting copper cell differentiation. In the anterior and posterior midgut, injury-induced BMP signaling acted autonomously in ISCs to limit proliferation and stem cell number after injury. Loss of BMP signaling pathway members in the midgut epithelium or loss of the BMP signaling ligand decapentaplegic from visceral muscle resulted in phenotypes similar to those described for juvenile polyposis syndrome, a human intestinal tumor caused by mutations in BMP signaling pathway components. Our data establish a new link between injury and hyperplasia and may provide insight into how BMP signaling mutations drive formation of human intestinal cancers.

Phosphorylation of the Smo tail is controlled by membrane localization and is dispensable for clustering

The Hedgehog (Hh) signalling cascade is highly conserved and involved in development and disease throughout evolution. Nevertheless, in comparison with other pathways our mechanistic understanding of Hh signal transduction is remarkably incomplete. In the absence of ligand, the Hh receptor Patched (Ptc) represses the key signal transducer Smoothened (Smo) through an unknown mechanism. Hh binding to Ptc alleviates this repression, causing Smo redistribution to the plasma membrane, phosphorylation and opening of the Smo cytoplasmic tail, and Smo oligomerization. However, the order and interdependence of these events is as yet poorly understood. We have mathematically modelled and simulated Smo activation for two alternative modes of pathway activation, with Ptc primarily affecting either Smo localization or phosphorylation. Visualizing Smo activation through a novel, fluorescence based reporter allowed us to test these competing models. Here we show that Smo localization to the plasma membrane is sufficient for phosphorylation of the cytoplasmic tail in the presence of Ptc. Using fluorescence cross-correlation spectroscopy (FCCS) we furthermore demonstrate that inactivation of Ptc by Hh induces Smo clustering irrespective of Smo phosphorylation. Our observations therefore support a model of Hh signal transduction whereby Smo subcellular localization and not phosphorylation is the primary target of Ptc function.

Dynamics and precision in retinoic acid morphogen gradients

Retinoic acid (RA) regulates many cellular behaviors during embryonic development and adult homeostasis. Like other morphogens, RA forms gradients through the use of localized sources and sinks, feedback, and interactions with other signals; this has been particularly well studied in the context of hindbrain segmentation in vertebrate embryos. Yet, as a small lipophilic molecule derived from a dietary source-vitamin A-RA differs markedly from better-studied polypeptide morphogens in its mechanisms of transport, signaling, and removal. Computational models suggest that the distinctive features of RA gradients make them particularly robust to large perturbations. Such features include combined positive and negative feedback effects via intracellular fatty acid binding proteins and RA-degrading enzymes. Here, we discuss how these features, together with feedback interactions among RA target genes, help enable RA to specify multiple, accurate pattern elements in the developing hindbrain, despite operating in an environment of high cellular and biochemical uncertainty and noise.

Encoding and decoding of positional information in morphogen-dependent patterning

Patterning during organogenesis is fundamentally realized through the interpretation of morphogen gradients by particular types of gene regulatory networks (GRNs). However, as quantitative studies have reported, spatial profiles of morphogen gradients include intra-embryo and inter-embryo variability, which could lead to errors in spatial recognition by cells and variations in patterning. By mathematically modeling the processes of generation and readout of spatial information - information encoding and decoding, by an analogy to computer communication - and maximizing the reproducibility of patterning against noise, the general designs of gradient profiles and their interpretation have been clarified. Furthermore, over the past few years, basic studies on patterning in more dynamic situations, that is, patterning in growing tissues with time-variant gradients, have been initiated. Here we provide an overview of patterning studies, pattern generating GRNs, concepts of information coding design for robust patterning, and patterning in growing tissues.

A Hh-driven gene network controls specification, pattern and size of the Drosophila simple eyes

During development, extracellular signaling molecules interact with intracellular gene networks to control the specification, pattern and size of organs. One such signaling molecule is Hedgehog (Hh). Hh is known to act as a morphogen, instructing different fates depending on the distance to its source. However, how Hh, when signaling across a cell field, impacts organ-specific transcriptional networks is still poorly understood. Here, we investigate this issue during the development of the Drosophila ocellar complex. The development of this sensory structure, which is composed of three simple eyes (or ocelli) located at the vertices of a triangular patch of cuticle on the dorsal head, depends on Hh signaling and on the definition of three domains: two areas of eya and so expression--the prospective anterior and posterior ocelli--and the intervening interocellar domain. Our results highlight the role of the homeodomain transcription factor engrailed (en) both as a target and as a transcriptional repressor of hh signaling in the prospective interocellar region. Furthermore, we identify a requirement for the Notch pathway in the establishment of en maintenance in a Hh-independent manner. Therefore, hh signals transiently during the specification of the interocellar domain, with en being required here for hh signaling attenuation. Computational analysis further suggests that this network design confers robustness to signaling noise and constrains phenotypic variation. In summary, using genetics and modeling we have expanded the ocellar gene network to explain how the interaction between the Hh gradient and this gene network results in the generation of stable mutually exclusive gene expression domains. In addition, we discuss some general implications our model may have in some Hh-driven gene networks.

Toward a systems-level understanding of the Hedgehog signaling pathway: defining the complex, robust, and fragile

The Hedgehog (Hh) signaling pathway plays a fundamental role in development and tissue homeostasis, governing cell proliferation and differentiation, as well as cell fate. Hh signaling is mediated by an intricate network of proteins that have positive and negative roles that work in concert to fine-tune signaling output. Using feedback loops, redundancy and subcellular compartmentalization, the temporal and spatial dynamics of Hh signaling have evolved to be complex and robust. Yet developmental defects and cancers that arise from perturbation of the Hh pathway reflect specific pathway fragilities. Importantly, these fragile nodes and edges present opportunities for the design of targeted therapies. Despite these significant advances, unconnected molecular links within the Hh pathway still remain, many of which revolve around the dependence of Hh signaling on the primary cilium, an antenna-like sensory organelle. A systems-level understanding of Hh signaling and of ciliary biology will comprehensively define all nodes and edges of the Hh signaling network and will help identify precise therapeutic targets.

The effect of the signalling scheme on the robustness of pattern formation in development

Pattern formation in development is a complex process which involves spatially distributed signals called morphogens that influence gene expression and thus the phenotypic identity of cells. Usually different cell types are spatially segregated, and the boundary between them may be determined by a threshold value of some state variable. The question arises as to how sensitive the location of such a boundary is to variations in properties, such as parameter values, that characterize the system. Here, we analyse both deterministic and stochastic reaction-diffusion models of pattern formation with a view towards understanding how the signalling scheme used for patterning affects the variability of boundary determination between cell types in a developing tissue.

Free extracellular diffusion creates the Dpp morphogen gradient of the Drosophila wing disc

BACKGROUND

How morphogen gradients form has long been a subject of controversy. The strongest support for the view that morphogens do not simply spread by free diffusion has come from a variety of studies of the Decapentaplegic (Dpp) gradient of the Drosophila larval wing disc.

RESULTS

In the present study, we initially show how the failure, in such studies, to consider the coupling of transport to receptor-mediated uptake and degradation has led to estimates of transport rates that are orders of magnitude too low, lending unwarranted support to a variety of hypothetical mechanisms, such as "planar transcytosis" and "restricted extracellular diffusion." Using several independent dynamic methods, we obtain data that are inconsistent with such models and show directly that Dpp transport occurs by simple, rapid diffusion in the extracellular space. We discuss the implications of these findings for other morphogen systems in which complex transport mechanisms have been proposed.

CONCLUSIONS

We believe that these findings resolve a major, longstanding question about morphogen gradient formation and provide a solid framework for interpreting experimental observations of morphogen gradient dynamics.

Gene regulatory logic for reading the Sonic Hedgehog signaling gradient in the vertebrate neural tube

Secreted signals, known as morphogens, provide the positional information that organizes gene expression and cellular differentiation in many developing tissues. In the vertebrate neural tube, Sonic Hedgehog (Shh) acts as a morphogen to control the pattern of neuronal subtype specification. Using an in vivo reporter of Shh signaling, mouse genetics, and systems modeling, we show that a spatially and temporally changing gradient of Shh signaling is interpreted by the regulatory logic of a downstream transcriptional network. The design of the network, which links three transcription factors to Shh signaling, is responsible for differential spatial and temporal gene expression. In addition, the network renders cells insensitive to fluctuations in signaling and confers hysteresis--memory of the signal. Our findings reveal that morphogen interpretation is an emergent property of the architecture of a transcriptional network that provides robustness and reliability to tissue patterning.

Dorsal-ventral gene expression in the Drosophila embryo reflects the dynamics and precision of the dorsal nuclear gradient

Patterning of the dorsal-ventral axis in the early Drosophila embryo depends on the nuclear distribution of the Dorsal transcription factor. Using live two-photon light-sheet microscopy, we quantified the nuclear Dorsal gradient in space and time and found that its amplitude and basal levels display oscillations throughout early embryonic development. These dynamics raise questions regarding how cells can reproducibly establish patterns of gene expression from a rapidly varying signal. We therefore quantified domains of Dorsal target genes, discovering their expression patterns are also dynamic. Computational modeling of this system reveals a correlation between Dorsal gradient dynamics and changes in target gene expression and suggests that these dynamics, together with time averaging of noise, results in the formation of graded gene expression borders in regions where the gradient is nearly flat. We propose that mRNA levels remain plastic during transient signaling events, allowing tissues to refine patterns in the face of genetic or environmental variation.

Distinct phosphorylations on kinesin costal-2 mediate differential hedgehog signaling strength

The graded Hedgehog (Hh) signal is transduced by the transmembrane Smoothened (Smo) proteins in both vertebrates and invertebrates. In Drosophila, associations between Smo and the Fused (Fu)/Costal-2 (Cos2)/Cubitus Interruptus (Ci) cytoplasmic complex lead to pathway activation, but it remains unclear how the cytoplasmic complex responds to and transduces different levels of Hh signaling. We show here that, within the Hh gradient field, low- and high-magnitude Smo activations control differentially the phosphorylation of Cos2 on two distinct serines. We also provide evidence that these phosphorylations depend on the Fu kinase activity and lead to a shift of Cos2 distribution from the cytoplasm to the plasma membrane. Moreover, the distinct Cos2 phosphorylation states mediate differential Hh signaling magnitude, suggesting that phosphorylation and relocation of Cos2 to the plasma membrane facilitate high-level Hh signaling through the control of Ci nuclear translocation and transcriptional activity.

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.

Gene length may contribute to graded transcriptional responses in the Drosophila embryo

An important question in developmental biology is how relatively shallow gradients of morphogens can reliably establish a series of distinct transcriptional readouts. Current models emphasize interactions between transcription factors binding in distinct modes to cis-acting sequences of target genes. Another recent idea is that the cis-acting interactions may amplify preexisting biases or prepatterns to establish robust transcriptional responses. In this study, we examine the possible contribution of one such source of prepattern, namely gene length. We developed quantitative imaging tools to measure gene expression levels for several loci at a time on a single-cell basis and applied these quantitative imaging tools to dissect the establishment of a gene expression border separating the mesoderm and neuroectoderm in the early Drosophila embryo. We first characterized the formation of a transient ventral-to-dorsal gradient of the Snail (Sna) repressor and then examined the relationship between this gradient and repression of neural target genes in the mesoderm. We found that neural genes are repressed in a nested pattern within a zone of the mesoderm abutting the neuroectoderm, where Sna levels are graded. While several factors may contribute to the transient graded response to the Sna gradient, our analysis suggests that gene length may play an important, albeit transient, role in establishing these distinct transcriptional responses. One prediction of the gene-length-dependent transcriptional patterning model is that the co-regulated genes knirps (a short gene) and knirps-related (a long gene) should be transiently expressed in domains of differing widths, which we confirmed experimentally. These findings suggest that gene length may contribute to establishing graded responses to morphogen gradients by providing transient prepatterns that are subsequently amplified and stabilized by traditional cis-regulatory interactions.

Morphogen gradients: from generation to interpretation

Morphogens are long-range signaling molecules that pattern developing tissues in a concentration-dependent manner. The graded activity of morphogens within tissues exposes cells to different signal levels and leads to region-specific transcriptional responses and cell fates. In its simplest incarnation, a morphogen signal forms a gradient by diffusion from a local source and clearance in surrounding tissues. Responding cells often transduce morphogen levels in a linear fashion, which results in the graded activation of transcriptional effectors. The concentration-dependent expression of morphogen target genes is achieved by their different binding affinities for transcriptional effectors as well as inputs from other transcriptional regulators. Morphogen distribution and interpretation are the result of complex interactions between the morphogen and responding tissues. The response to a morphogen is dependent not simply on morphogen concentration but also on the duration of morphogen exposure and the state of the target cells. In this review, we describe the morphogen concept and discuss the mechanisms that underlie the generation, modulation, and interpretation of morphogen gradients.

DSulfatase-1 fine-tunes Hedgehog patterning activity through a novel regulatory feedback loop

Sulfs are secreted sulfatases that catalyse removal of sulfate from Heparan Sulfate Proteoglycans (HSPGs) in the extracellular space. These enzymes are well known to regulate a number of crucial signalling pathways during development. In this study, we report that DSulfatase-1 (DSulf1), the unique Drosophila Sulf protein, is a regulator of Hedgehog (Hh) signalling during wing development. DSulf1 activity is required in both Hh source and Hh receiving cells for proper positioning of Hh target gene expression boundaries. As assessed by loss- and gain-of-function experiments in specific compartments, DSulf1 displays dual functions with respect to Hh signalling, acting as a positive regulator in Hh producing cells and a negative regulator in Hh receiving cells. In either domain, DSulf1 modulates Hh distribution by locally lowering the concentration of the morphogen at the apical pole of wing disc cells. Thus, we propose that DSulf1, by its desulfation catalytic activity, lowers Hh/HSPG interaction in both Hh source and target fields, thereby enhancing Hh release from its source of production and reducing Hh signalling activity in responding cells. Finally, we show that Dsulf1 pattern of expression is temporally regulated and depends on EGFR signalling, a Hh-dependent secondary signal in this tissue. Our data reveal a novel Hh regulatory feedback loop, involving DSulf1, which contributes to maintain and stabilise expression domains of Hh target genes during wing disc development.

Analysis of mutants with altered shh activity and posterior digit loss supports a biphasic model for shh function as a morphogen and mitogen

Sonic hedgehog (Shh) controls the number and type of digits formed. Using a conditional genetic approach for timed removal of Shh, we previously proposed a biphasic model of Shh function: a transient patterning phase, during which digit progenitors are specified, and an extended proliferative phase, during which expansion of progenitor pools enables digit formation. Other models favor a close integration of digit patterning and expansion, with sequential promotion to more posterior identity over time, apparently supported by some mutants with selective posterior digit loss. To further test these models, we analyzed the dynamics of Shh activity in several oligodactylous mutants with different types of digit loss. The profile of Shh activity and phenotypic outcome in these mutants supports a biphasic over an integrated temporal model. Eomesodermin expression, as an independent marker of posterior digit identity, confirmed that proper digit 4 specification requires only the transient phase of Shh activity.

Pattern, growth, and control

Systems biology seeks not only to discover the machinery of life but to understand how such machinery is used for control, i.e., for regulation that achieves or maintains a desired, useful end. This sort of goal-directed, engineering-centered approach also has deep historical roots in developmental biology. Not surprisingly, developmental biology is currently enjoying an influx of ideas and methods from systems biology. This Review highlights current efforts to elucidate design principles underlying the engineering objectives of robustness, precision, and scaling as they relate to the developmental control of growth and pattern formation. Examples from vertebrate and invertebrate development are used to illustrate general lessons, including the value of integral feedback in achieving set-point control; the usefulness of self-organizing behavior; the importance of recognizing and appropriately handling noise; and the absence of "free lunch." By illuminating such principles, systems biology is helping to create a functional framework within which to make sense of the mechanistic complexity of organismal development.

Steady-state invariant genetics: probing the role of morphogen gradient dynamics in developmental patterning

Morphogen-mediated patterning is the predominant mechanism by which positional information is established during animal development. In the classical view, the interpretation of positional signals depends on the equilibrium distribution of a morphogen, regardless of the dynamics of gradient formation. The problem of whether or not morphogen dynamics contribute to developmental patterning has not been explored in detail, partly because genetic experiments, which selectively affect signalling dynamics while maintaining unchanged the steady-state morphogen profile, are difficult to design and interpret. Here, I present a modelling-based approach to identify genetic mutations in developmental patterning that may affect the transient, but leave invariant the steady-state signalling gradient. As a case study, this approach is used to explore the dynamic properties of Hedgehog (Hh) signalling in the developing wing of the fruitfly, Drosophila melanogaster. This analysis provides insights into how different properties of the Hh gradient dynamics, such as the duration of exposure to the signal or the maximum width of the transient gradient, can be genetically perturbed without affecting the steady-state distribution of the Hh concentration profile. I propose that this method can be used as an experimental design tool to investigate the role of transient morphogen gradients in developmental patterning and discuss the generality of these ideas in other problems.