Dpp gradient formation by dynamin-dependent endocytosis: receptor trafficking and the diffusion model

Statistical physics of inhomogeneous transport: Unification of diffusion laws and inference from first-passage statistics

Characterization of composite materials, whose properties vary in space over microscopic scales, has become a problem of broad interdisciplinary interest. In particular, estimation of the inhomogeneous transport coefficients, e.g., the diffusion coefficient or the heat conductivity, which shape important processes in biology and engineering, is a challenging task. The analysis of such systems is further complicated because two alternative formulations of the inhomogeneous transport equations exist in the literature-the Smoluchowski and Fokker-Planck equations, which are also related to the so-called Ito-Stratonovich dilemma. Using the theory of statistical physics, we show that the two formulations, usually regarded as distinct models, are physically equivalent. From this result we develop efficient estimates for the transverse space-dependent diffusion coefficient in fluids near a phase boundary. Our method requires only measurements of escape probabilities and mean exit times of molecules leaving a narrow spatial region. We test our estimates in three case studies: (i) a Langevin model of a Büttikker-Landauer ratchet; atomistic molecular-dynamics simulations of liquid-water molecules in contact with (ii) vapor, and (iii) soap (surfactant) film which has promising applications in physical chemistry. Our analysis reveals that near the surfactant monolayer the mobility of water molecules is slowed down almost twice with respect to the bulk liquid. Moreover, the diffusion coefficient of water correlates with the transition from hydrophilic to hydrophobic parts of the film.

Generation of extracellular morphogen gradients: the case for diffusion

Cells within developing tissues rely on morphogens to assess positional information. Passive diffusion is the most parsimonious transport model for long-range morphogen gradient formation but does not, on its own, readily explain scaling, robustness and planar transport. Here, we argue that diffusion is sufficient to ensure robust morphogen gradient formation in a variety of tissues if the interactions between morphogens and their extracellular binders are considered. A current challenge is to assess how the affinity for extracellular binders, as well as other biophysical and cell biological parameters, determines gradient dynamics and shape in a diffusion-based transport system. Technological advances in genome editing, tissue engineering, live imaging and in vivo biophysics are now facilitating measurement of these parameters, paving the way for mathematical modelling and a quantitative understanding of morphogen gradient formation and modulation.

To be more precise: the role of intracellular trafficking in development and pattern formation

Living cells interpret a variety of signals in different contexts to elucidate functional responses. While the understanding of signalling molecules, their respective receptors and response at the gene transcription level have been relatively well-explored, how exactly does a single cell interpret a plethora of time-varying signals? Furthermore, how their subsequent responses at the single cell level manifest in the larger context of a developing tissue is unknown. At the same time, the biophysics and chemistry of how receptors are trafficked through the complex dynamic transport network between the plasma membrane-endosome-lysosome-Golgi-endoplasmic reticulum are much more well-studied. How the intracellular organisation of the cell and inter-organellar contacts aid in orchestrating trafficking, as well as signal interpretation and modulation by the cells are beginning to be uncovered. In this review, we highlight the significant developments that have strived to integrate endosomal trafficking, signal interpretation in the context of developmental biology and relevant open questions with a few chosen examples. Furthermore, we will discuss the imaging technologies that have been developed in the recent past that have the potential to tremendously accelerate knowledge gain in this direction while shedding light on some of the many challenges.

Genome-Wide Differential DNA Methylation in Reproductive, Morphological, and Visual System Differences Between Queen Bee and Worker Bee (Apis mellifera)

There are many differences in external morphology and internal physiology between the Apis mellifera queen bee and worker bee, some of which are relevant to beekeeping production. These include reproductive traits, body size, royal jelly secreting properties, and visual system development, among others. The identification of candidate genes that control the differentiation of these traits is critical for selective honeybee breeding programs. In this study, we compared the genomic methylation of queen bee and worker bee larvae at 3, 4, and 5 days of age by whole-genome bisulfite sequencing, and found that the basic characteristics of genomic methylation in queen and worker larvae were the same. There were approximately 49 million cytosines in the Apis larvae genome, of which about 90,000 were methylated. Methylated CpG sites accounted for 99% of the methylated cytosines, and methylation mainly occurred in exons. However, methylation levels of queen and worker larvae showed different trends with age: the methylation level of queen larvae varied with age in an inverted parabola, while the corresponding trend for worker larvae with resembled an exponential curve with a platform. The methylation level of queen larvae was higher than that of worker larvae at 3 days of age, lower than that of worker larvae at 4 days of age, and similar to that of worker larvae at 5 days old. The top 10 differentially methylated genes (DMGs) and 13 caste-specific methylated genes were listed, and correlations with caste determination were speculated. We additionally screened 38 DMGs between queen larvae and worker larvae involved in specific organ differentiation as well as reproduction, morphology, and vision differentiation during caste determination. These genes are potential molecular markers for selective breeding of A. mellifera to improve fecundity, royal jelly production, body size, and foraging, and represent candidate genes for investigating specialized functional segregation during the process of caste differentiation.

Interplay between morphogen-directed positional information systems and physiological signaling

The development of an organism from an undifferentiated single cell into a spatially complex structure requires spatial patterning of cell fates across tissues. Positional information, proposed by Lewis Wolpert in 1969, has led to the characterization of many components involved in regulating morphogen signaling activity. However, how morphogen gradients are established, maintained, and interpreted by cells still is not fully understood. Quantitative and systems-based approaches are increasingly needed to define general biological design rules that govern positional information systems in developing organisms. This short review highlights a selective set of studies that have investigated the roles of physiological signaling in modulating and mediating morphogen-based pattern formation. Similarities between neural transmission and morphogen-based pattern formation mechanisms suggest underlying shared principles of active cell-based communication. Within larger tissues, neural networks provide directed information, via physiological signaling, that supplements positional information through diffusion. Further, mounting evidence demonstrates that physiological signaling plays a role in ensuring robustness of morphogen-based signaling. We conclude by highlighting several outstanding questions regarding the role of physiological signaling in morphogen-based pattern formation. Elucidating how physiological signaling impacts positional information is critical for understanding the close coupling of developmental and cellular processes in the context of development, disease, and regeneration.

Optogenetic approaches to investigate spatiotemporal signaling during development

Embryogenesis is coordinated by signaling pathways that pattern the developing organism. Many aspects of this process are not fully understood, including how signaling molecules spread through embryonic tissues, how signaling amplitude and dynamics are decoded, and how multiple signaling pathways cooperate to pattern the body plan. Optogenetic approaches can be used to address these questions by providing precise experimental control over a variety of biological processes. Here, we review how these strategies have provided new insights into developmental signaling and discuss how they could contribute to future investigations.

Bidirectional transport model of morphogen gradient formation via cytonemes

Morphogen protein gradients play an important role in the spatial regulation of patterning during embryonic development. The most commonly accepted mechanism for gradient formation is diffusion from a source combined with degradation. Recently, there has been growing interest in an alternative mechanism, which is based on the direct delivery of morphogens along thin, actin-rich cellular extensions known as cytonemes. In this paper, we develop a bidirectional motor transport model for the flux of morphogens along cytonemes, linking a source cell to a one-dimensional array of target cells. By solving the steady-state transport equations, we show how a morphogen gradient can be established, and explore how the mean velocity of the motors affects properties of the morphogen gradient such as accumulation time and robustness. In particular, our analysis suggests that in order to achieve robustness with respect to changes in the rate of synthesis of morphogen, the mean velocity has to be negative, that is, retrograde flow or treadmilling dominates. Thus the potential targeting precision of cytonemes comes at an energy cost. We then study the effects of non-uniformly allocating morphogens to the various cytonemes projecting from a source cell. This competition for resources provides a potential regulatory control mechanism not available in diffusion-based models.

Scaling of pattern formations and morphogen gradients

The concentration gradient of morphogens provides positional information for an embryo and plays a pivotal role in pattern formation of tissues during the developmental processes. Morphogen-dependent pattern formations show robustness despite various perturbations. Although tissues usually grow and dynamically change their size during histogenesis, proper patterns are formed without the influence of size variations. Furthermore, even when the blastula embryo of Xenopus laevis is bisected into dorsal and ventral halves, the dorsal half of the embryo leads to proportionally patterned half-sized embryos. This robustness of pattern formation despite size variations is termed as scaling. In this review, I focused on the morphogen-dependent dorsal-ventral axis formation in Xenopus and described how morphogens form a proper gradient shape according to the embryo size.

Extracellular interactions and ligand degradation shape the nodal morphogen gradient

The correct distribution and activity of secreted signaling proteins called morphogens is required for many developmental processes. Nodal morphogens play critical roles in embryonic axis formation in many organisms. Models proposed to generate the Nodal gradient include diffusivity, ligand processing, and a temporal activation window. But how the Nodal morphogen gradient forms in vivo remains unclear. Here, we have measured in vivo for the first time, the binding affinity of Nodal ligands to their major cell surface receptor, Acvr2b, and to the Nodal inhibitor, Lefty, by fluorescence cross-correlation spectroscopy. We examined the diffusion coefficient of Nodal ligands and Lefty inhibitors in live zebrafish embryos by fluorescence correlation spectroscopy. We also investigated the contribution of ligand degradation to the Nodal gradient. We show that ligand clearance via degradation shapes the Nodal gradient and correlates with its signaling range. By computational simulations of gradient formation, we demonstrate that diffusivity, extra-cellular interactions, and selective ligand destruction collectively shape the Nodal morphogen gradient.

DOI:http://dx.doi.org/10.7554/eLife.13879.001

Animals develop from a single fertilized egg cell into multicellular organisms. This process requires chemical signals called “morphogens” that instruct the cells how to behave during development. The morphogens move across cells and tissues to form gradients of the signal. Cells then respond in different ways depending on how much of the signal they receive. This, in turn, depends on several factors: first, how quickly or slowly the signal moves; second, how well the morphogen binds to responding cells and other molecules in its path; and third, how much signal is lost or destroyed during the movement.

Many researchers study morphogen gradients in the transparent zebrafish, since it grows quickly and it is easy to see developmental changes. However, until now it was not fully clear how the well-known morphogen called Nodal moves in live zebrafish as they develop.

Wang, Wang et al. have now investigated how well Nodal signals bind to the surface of cells that receive the signal and to a molecule called “Lefty”, which is present in the same path and interferes with Nodal signals. Advanced techniques called fluorescence correlation and cross-correlation spectroscopy were used to measure Nodal signals at the level of single molecules in growing zebrafish. The experiments gave insights into how far Nodal signals move and remain active. The results showed that, in addition to Nodal diffusing and binding to receiving cells, one of the most important factors determining how far and quickly Nodal moves is its inactivation and destruction. Lastly, Wang, Wang et al. built computational models to test their observations from live zebrafish.

The current work was based on forcing zebrafish to produce molecules including Nodal at locations within the fish that normally do not make them. Therefore future experiments will aim to examine these molecules and their interactions when they are produced at their normal locations in the animal over time.

DOI:http://dx.doi.org/10.7554/eLife.13879.002

Morphogen transport: theoretical and experimental controversies

According to morphogen gradient theory, extracellular ligands produced from a localized source convey positional information to receiving cells by signaling in a concentration-dependent manner. How do morphogens create concentration gradients to establish positional information in developing tissues? Surprisingly, the answer to this central question remains largely unknown. During development, a relatively small number of morphogens are reiteratively deployed to ensure normal embryogenesis and organogenesis. Thus, the intracellular processing and extracellular transport of morphogens are tightly regulated in a tissue-specific manner. Over the past few decades, diverse experimental and theoretical approaches have led to numerous conflicting models for gradient formation. In this review, we summarize the experimental evidence for each model and discuss potential future directions for studies of morphogen gradients. For further resources related to this article, please visit the WIREs website.

CONFLICT OF INTEREST

The authors have declared no conflicts of interest for this article.

Coordination of patterning and growth by the morphogen DPP

The elegance of animal body plans derives from an intimate connection between function and form, which during organ formation is linked to patterning and growth. Yet, how patterning and growth are coordinated still remains largely a mystery. To study this question the Drosophila wing imaginal disc, an epithelial primordial organ that later forms the adult wing, has proven to be an invaluable and versatile model. Wing disc development is organized around a coordinate system provided by morphogens such as the TGF-β homolog Decapentaplegic (DPP). The function of DPP has been studied at multiple levels: ranging from the kinetics of gradient formation to the establishment and maintenance of target gene domains as well as DPP's role in growth control. Here, we focus on recent publications that both enrich our view of DPP signaling but also highlight outstanding questions of how DPP coordinates patterning and growth during development.

Mathematical analysis on a multidimensional model of morphogen transport with receptor synthesis

In biological development, morphogens are locally produced and spread to other regions in organs, forming gradients that control the inter-related pattern and growth of developing organs. Mechanisms of morphogen transport were built and investigated by numerical simulations in [A. D. Lander, Q. Nie and F. Y. M. Wan, Do morphogen gradients arise by diffusion? Developmental Cell2 (2002) 785–796]. In that paper, model C, which considers endocytosis, exocytosis and receptor synthesis and degradation, is in a one-dimensional spatial region and couples a partial differential equation with ordinary differential equations. Here, this model is promoted to an arbitrary dimension bounded region. We prove existence, uniqueness and non-negativity of a global solution for this advanced model, of its steady-state solution and linear stability of steady state by operator semigroup, the Schauder theorem and local perturbation method. Our results improve previous results for this model in a one dimension region.

The role of endocytosis during morphogenetic signaling

Morphogens are signaling molecules that are secreted by a localized source and spread in a target tissue where they are involved in the regulation of growth and patterning. Both the activity of morphogenetic signaling and the kinetics of ligand spreading in a tissue depend on endocytosis and intracellular trafficking. Here, we review quantitative approaches to study how large-scale morphogen profiles and signals emerge in a tissue from cellular trafficking processes and endocytic pathways. Starting from the kinetics of endosomal networks, we discuss the role of cellular trafficking and receptor dynamics in the formation of morphogen gradients. These morphogen gradients scale during growth, which implies that overall tissue size influences cellular trafficking kinetics. Finally, we discuss how such morphogen profiles can be used to control tissue growth. We emphasize the role of theory in efforts to bridge between scales.

Strategies for exploring TGF-β signaling in Drosophila

The TGF-β pathway is an evolutionarily conserved signal transduction module that mediates diverse biological processes in animals. In Drosophila, both the BMP and Activin branches are required for viability. Studies rooted in classical and molecular genetic approaches continue to uncover new developmental roles for TGF-β signaling. We present an overview of the secreted ligands, transmembrane receptors and cellular Smad transducer proteins that compose the core pathway in Drosophila. An assortment of tools have been developed to conduct tissue-specific loss- and gain-of-function experiments for these pathway components. We discuss the deployment of these reagents, with an emphasis on appropriate usage and limitations of the available tools. Throughout, we note reagents that are in need of further improvement or development, and signaling features requiring further study. A general theme is that comparison of phenotypes for ligands, receptors, and Smads can be used to map tissue interactions, and to separate canonical and non-canonical signaling activities. Core TGF-β signaling components are subject to multiple layers of regulation, and are coupled to context-specific inputs and outputs. In addition to fleshing out how TGF-β signaling serves the fruit fly, we anticipate that future studies will uncover new regulatory nodes and modes and will continue to advance paradigms for how TGF-β signaling regulates general developmental processes.

Mechanisms of scaling in pattern formation

Many organisms and their constituent tissues and organs vary substantially in size but differ little in morphology; they appear to be scaled versions of a common template or pattern. Such scaling involves adjusting the intrinsic scale of spatial patterns of gene expression that are set up during development to the size of the system. Identifying the mechanisms that regulate scaling of patterns at the tissue, organ and organism level during development is a longstanding challenge in biology, but recent molecular-level data and mathematical modeling have shed light on scaling mechanisms in several systems, including Drosophila and Xenopus. Here, we investigate the underlying principles needed for understanding the mechanisms that can produce scale invariance in spatial pattern formation and discuss examples of systems that scale during development.

Dual delayed feedback provides sensitivity and robustness to the NF-κB signaling module

Many cellular stress-responsive signaling systems exhibit highly dynamic behavior with oscillatory features mediated by delayed negative feedback loops. What remains unclear is whether oscillatory behavior is the basis for a signaling code based on frequency modulation (FM) or whether the negative feedback control modules have evolved to fulfill other functional requirements. Here, we use experimentally calibrated computational models to interrogate the negative feedback loops that regulate the dynamic activity of the transcription factor NF-κB. Linear stability analysis of the model shows that oscillatory frequency is a hard-wired feature of the primary negative feedback loop and not a function of the stimulus, thus arguing against an FM signaling code. Instead, our modeling studies suggest that the two feedback loops may be tuned to provide for rapid activation and inactivation capabilities for transient input signals of a wide range of durations; by minimizing late phase oscillations response durations may be fine-tuned in a graded rather than quantized manner. Further, in the presence of molecular noise the dual delayed negative feedback system minimizes stochastic excursions of the output to produce a robust NF-κB response.

ROBUSTNESS OF MORPHOGEN GRADIENTS WITH "BUCKET BRIGADE" TRANSPORT THROUGH MEMBRANE-ASSOCIATED NON-RECEPTORS

Robust multiple-fate morphogen gradients are essential for embryo development. Here, we analyze mathematically a model of morphogen gradient (such as Dpp in Drosophila wing imaginal disc) formation in the presence of non-receptors with both diffusion of free morphogens and the movement of morphogens bound to non-receptors. Under the assumption of rapid degradation of unbound morphogen, we introduce a method of functional boundary value problem and prove the existence, uniqueness and linear stability of a biologically acceptable steady-state solution. Next, we investigate the robustness of this steady-state solution with respect to significant changes in the morphogen synthesis rate. We prove that the model is able to produce robust biological morphogen gradients when production and degradation rates of morphogens are large enough and non-receptors are abundant. Our results provide mathematical and biological insight to a mechanism of achieving stable robust long distance morphogen gradients. Key elements of this mechanism are rapid turnover of morphogen to non-receptors of neighoring cells resulting in significant degradation and transport of non-receptor-morphogen complexes, the latter moving downstream through a "bucket brigade" process.

Morphogen transport

The graded distribution of morphogens underlies many of the tissue patterns that form during development. How morphogens disperse from a localized source and how gradients in the target tissue form has been under debate for decades. Recent imaging studies and biophysical measurements have provided evidence for various morphogen transport models ranging from passive mechanisms, such as free or hindered extracellular diffusion, to cell-based dispersal by transcytosis or cytonemes. Here, we analyze these transport models using the morphogens Nodal, fibroblast growth factor and Decapentaplegic as case studies. We propose that most of the available data support the idea that morphogen gradients form by diffusion that is hindered by tortuosity and binding to extracellular molecules.

How cells know where they are

Development, regeneration, and even day-to-day physiology require plant and animal cells to make decisions based on their locations. The principles by which cells may do this are deceptively straightforward. But when reliability needs to be high--as often occurs during development--successful strategies tend to be anything but simple. Increasingly, the challenge facing biologists is to relate the diverse diffusible molecules, control circuits, and gene regulatory networks that help cells know where they are to the varied, sometimes stringent, constraints imposed by the need for real-world precision and accuracy.

Investigating the principles of morphogen gradient formation: from tissues to cells

Morphogen gradients regulate the patterning and growth of many tissues, hence a key question is how they are established and maintained during development. Theoretical descriptions have helped to explain how gradient shape is controlled by the rates of morphogen production, spreading and degradation. These effective rates have been measured using fluorescence recovery after photobleaching (FRAP) and photoactivation. To unravel which molecular events determine the effective rates, such tissue-level assays have been combined with genetic analysis, high-resolution assays, and models that take into account interactions with receptors, extracellular components and trafficking. Nevertheless, because of the natural and experimental data variability, and the underlying assumptions of transport models, it remains challenging to conclusively distinguish between cellular mechanisms.

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.

Extracellular movement of signaling molecules

Extracellular signaling molecules have crucial roles in development and homeostasis, and their incorrect deployment can lead to developmental defects and disease states. Signaling molecules are released from sending cells, travel to target cells, and act over length scales of several orders of magnitude, from morphogen-mediated patterning of small developmental fields to hormonal signaling throughout the organism. We discuss how signals are modified and assembled for transport, which routes they take to reach their targets, and how their range is affected by mobility and stability.

Understanding morphogenetic growth control -- lessons from flies

Morphogens are secreted signalling molecules that control the patterning and growth of developing organs. How morphogens regulate patterning is fairly well understood; however, how they control growth is less clear. Four principal models have been proposed to explain how the morphogenetic protein Decapentaplegic (DPP) controls the growth of the wing imaginal disc in the fly. Recent studies in this model system have provided a wealth of experimental data on growth and DPP gradient properties, as well as on the interactions of DPP with other signalling pathways. These findings have allowed a more precise formulation and evaluation of morphogenetic growth models. The insights into growth control by the DPP gradient will also be useful for understanding other morphogenetic growth systems.

Local BMP receptor activation at adherens junctions in the Drosophila germline stem cell niche

According to the stem cell niche synapse hypothesis postulated for the mammalian haematopoietic system, spatial specificity of niche signals is maximized by subcellularly restricting signalling to cadherin-based adherens junctions between individual niche and stem cells. However, such a synapse has never been observed directly, in part, because tools to detect active growth factor receptors with subcellular resolution were not available. Here we describe a novel fluorescence-based reporter that directly visualizes bone morphogenetic protein (BMP) receptor activation and show that in the Drosophila testis a BMP niche signal is transmitted preferentially at adherens junctions between hub and germline stem cells, resembling the proposed synapse organization. Ligand secretion involves the exocyst complex and the Rap activator Gef26, both of which are also required for Cadherin trafficking towards adherens junctions. We, therefore, propose that local generation of the BMP signal is achieved through shared use of the Cadherin transport machinery.

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.

Formation of the long range Dpp morphogen gradient

The TGF-β homolog Decapentaplegic (Dpp) acts as a secreted morphogen in the Drosophila wing disc, and spreads through the target tissue in order to form a long range concentration gradient. Despite extensive studies, the mechanism by which the Dpp gradient is formed remains controversial. Two opposing mechanisms have been proposed: receptor-mediated transcytosis (RMT) and restricted extracellular diffusion (RED). In these scenarios the receptor for Dpp plays different roles. In the RMT model it is essential for endocytosis, re-secretion, and thus transport of Dpp, whereas in the RED model it merely modulates Dpp distribution by binding it at the cell surface for internalization and subsequent degradation. Here we analyzed the effect of receptor mutant clones on the Dpp profile in quantitative mathematical models representing transport by either RMT or RED. We then, using novel genetic tools, experimentally monitored the actual Dpp gradient in wing discs containing receptor gain-of-function and loss-of-function clones. Gain-of-function clones reveal that Dpp binds in vivo strongly to the type I receptor Thick veins, but not to the type II receptor Punt. Importantly, results with the loss-of-function clones then refute the RMT model for Dpp gradient formation, while supporting the RED model in which the majority of Dpp is not bound to Thick veins. Together our results show that receptor-mediated transcytosis cannot account for Dpp gradient formation, and support restricted extracellular diffusion as the main mechanism for Dpp dispersal. The properties of this mechanism, in which only a minority of Dpp is receptor-bound, may facilitate long-range distribution.

Morphogens are signaling molecules that trigger specific responses in cells in a concentration-dependent manner. The formation of morphogen gradients is essential for the patterning of tissues and organs. Decapentaplegic (Dpp) is the Drosophila homolog of the bone morphogenic proteins in vertebrates and forms a morphogen gradient along the anterior-posterior axis of the Drosophila wing imaginal disc, a single-cell layered epithelium. Dpp determines the growth and final size of the wing disc and serves as an ideal model system to study gradient formation. Despite extensive studies the mechanism by which morphogen gradients are established remains controversial. In the case of Dpp two mechanisms have been postulated, namely extracellular diffusion and receptor-mediated transcytosis. In the first model Dpp is suggested to move by diffusion through the extracellular matrix of a tissue, whereas in the latter model Dpp is transported through the cells by receptor-mediated uptake and re-secretion. In this work we combined novel genetic tools with mathematical modeling to discriminate between the two models. Our results suggest that the Dpp gradient forms following the extracellular diffusion mechanism. Moreover, our data suggest that the majority of the extracellular Dpp is free and not bound to its receptor, a property likely to play a role for the long-range gradient formation.

A dynamical model of ommatidial crystal formation

The crystalline photoreceptor lattice in the Drosophila eye is a paradigm for pattern formation during development. During eye development, activation of proneural genes at a moving front adds new columns to a regular lattice of R8 photoreceptors. We present a mathematical model of the governing activator-inhibitor system, which indicates that the dynamics of positive induction play a central role in the selection of certain cells as R8s. The "switch and template" patterning mechanism we observe is mathematically very different from the well-known Turing instability. Unlike a standard lateral inhibition model, our picture implies that R8s are defined before the appearance of the complete group of proneural cells. The model reproduces the full time course of proneural gene expression and accounts for specific features of the refinement of proneural groups that had resisted explanation. It moreover predicts that perturbing the normal template can lead to eyes containing stripes of R8 cells. We observed these stripes experimentally after manipulation of the Notch and scabrous genes. Our results suggest an alternative to the generally assumed mode of operation for lateral inhibition during development; more generally, they hint at a broader role for bistable switches in the initial establishment of patterns as well as in their maintenance.

Formation of morphogen gradients: local accumulation time

Spatial regulation of cell differentiation in embryos can be provided by morphogen gradients, which are defined as the concentration fields of molecules that control gene expression. For example, a cell can use its surface receptors to measure the local concentration of an extracellular ligand and convert this information into a corresponding change in its transcriptional state. We characterize the time needed to establish a steady-state gradient in problems with diffusion and degradation of locally produced chemical signals. A relaxation function is introduced to describe how the morphogen concentration profile approaches its steady state. This function is used to obtain a local accumulation time that provides a time scale that characterizes relaxation to steady state at an arbitrary position within the patterned field. To illustrate the approach we derive local accumulation times for a number of commonly used models of morphogen gradient formation.

Quantification of biological interactions with particle image cross-correlation spectroscopy (PICCS)

A multitude of biological processes that involve multiple interaction partners are observed by two-color microscopy. Here we describe an analysis method for the robust quantification of correlation between signals in different color channels: particle image cross-correlation spectroscopy (PICCS). The method, which exploits the superior positional accuracy obtained in single-object and single-molecule microscopy, can extract the correlation fraction and length scale. We applied PICCS to correlation measurements in living tissues. The morphogen Decapentaplegic (Dpp) was imaged in wing imaginal disks of fruit fly larvae and we quantified what fraction of early endosomes contained Dpp.

When it pays to rush: interpreting morphogen gradients prior to steady-state

During development, morphogen gradients precisely determine the position of gene expression boundaries despite the inevitable presence of fluctuations. Recent experiments suggest that some morphogen gradients may be interpreted prior to reaching steady-state. Theoretical work has predicted that such systems will be more robust to embryo-to-embryo fluctuations. By analyzing two experimentally motivated models of morphogen gradient formation, we investigate the positional precision of gene expression boundaries determined by pre-steady-state morphogen gradients in the presence of embryo-to-embryo fluctuations, internal biochemical noise and variations in the timing of morphogen measurement. Morphogens that are direct transcription factors are found to be particularly sensitive to internal noise when interpreted prior to steady-state, disadvantaging early measurement, even in the presence of large embryo-to-embryo fluctuations. Morphogens interpreted by cell-surface receptors can be measured prior to steady-state without significant decrease in positional precision provided fluctuations in the timing of measurement are small. Applying our results to experiment, we predict that Bicoid, a transcription factor morphogen in Drosophila, is unlikely to be interpreted prior to reaching steady-state. We also predict that Activin in Xenopus and Nodal in zebrafish, morphogens interpreted by cell-surface receptors, can be decoded in pre-steady-state.

The extracellular regulation of bone morphogenetic protein signaling

In many cases, the level, positioning and timing of signaling through the bone morphogenetic protein (BMP) pathway are regulated by molecules that bind BMP ligands in the extracellular space. Whereas many BMP-binding proteins inhibit signaling by sequestering BMPs from their receptors, other BMP-binding proteins cause remarkably context-specific gains or losses in signaling. Here, we review recent findings and hypotheses on the complex mechanisms that lead to these effects, with data from developing systems, biochemical analyses and mathematical modeling.

Morphogen gradient formation

How morphogen gradients are formed in target tissues is a key question for understanding the mechanisms of morphological patterning. Here, we review different mechanisms of morphogen gradient formation from theoretical and experimental points of view. First, a simple, comprehensive overview of the underlying biophysical principles of several mechanisms of gradient formation is provided. We then discuss the advantages and limitations of different experimental approaches to gradient formation analysis.

Analysis of dynamic morphogen scale invariance

During the development of some tissues, fields of multipotent cells differentiate into distinct cell types in response to the local concentration of a signalling factor called a morphogen. Typically, individual organisms within a population differ in size, but their body plans appear to be scaled versions of a common template. Similarly, closely related species may differ by three or more orders of magnitude in size, yet common structures between species scale to have similar proportions. In standard reaction-diffusion equations, the morphogen range has a length scale that depends on a balance between kinetic and transport processes and not on the length or size of the field of cells being patterned. However, as shown here for a class of morphogen-patterning systems, a number of conditions lead to scale invariance of the morphogen distribution at equilibrium and during the transient approach to equilibrium. Equilibrium scale invariance requires conservation of the total binding site number and total input flux. Dynamic scale invariance additionally requires sufficient binding to slow the diffusion of ligand. The equations derived herein can be extended to the study of other perturbations to gain further insight into the processes regulating the robustness and scaling of morphogen-mediated pattern formation.

Precision of the Dpp gradient

Morphogen concentration gradients provide positional information by activating target genes in a concentration-dependent manner. Recent reports show that the gradient of the syncytial morphogen Bicoid seems to provide precise positional information to determine target gene domains. For secreted morphogenetic ligands, the precision of the gradients, the signal transduction and the reliability of target gene expression domains have not been studied. Here we investigate these issues for the TGF-beta-type morphogen Dpp. We first studied theoretically how cell-to-cell variability in the source, the target tissue, or both, contribute to the variations of the gradient. Fluctuations in the source and target generate a local maximum of precision at a finite distance to the source. We then determined experimentally in the wing epithelium: (1) the precision of the Dpp concentration gradient; (2) the precision of the Dpp signaling activity profile; and (3) the precision of activation of the Dpp target gene spalt. As captured by our theoretical description, the Dpp gradient provides positional information with a maximal precision a few cells away from the source. This maximal precision corresponds to a positional uncertainly of about a single cell diameter. The precision of the Dpp gradient accounts for the precision of the spalt expression range, implying that Dpp can act as a morphogen to coarsely determine the expression pattern of target genes.

Theoretical and experimental approaches to understand morphogen gradients

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

The Decapentaplegic morphogen gradient: a precise definition

Two key processes are in the basis of morphogenesis: the spatial allocation of cell types in fields of naïve cells and the regulation of growth. Both are controlled by morphogens, which activate target genes in the growing tissue in a concentration-dependent manner. Thus the morphogen model is an intrinsically quantitative concept. However, quantitative studies were performed only in recent years on two morphogens: Bicoid and Decapentaplegic. This review covers quantitative aspects of the formation and precision of the Decapentaplegic morphogen gradient. The morphogen gradient concept is transitioning from a soft definition to a precise idea of what the gradient could really do.

Activator-inhibitor dynamics of vertebrate limb pattern formation

The development of the vertebrate limb depends on an interplay of cellular differentiation, pattern formation, and tissue morphogenesis on multiple spatial and temporal scales. While numerous gene products have been described that participate in, and influence, the generation of the limb skeletal pattern, an understanding of the most salient feature of the developing limb--its quasiperiodic arrangement of bones, requires additional organizational principles. We review several such principles, drawing on concepts of physics and chemical dynamics along with molecular genetics and cell biology. First, a "core mechanism" for precartilage mesenchymal condensation is described, based on positive autoregulation of the morphogen transforming growth factor (TGF)-beta, induction of the extracellular matrix (ECM) protein fibronectin, and focal accumulation of cells via haptotaxis. This core mechanism is shown to be part of a local autoactivation-lateral inhibition (LALI) system that ensures that the condensations will be regularly spaced. Next, a "bare-bones" model for limb development is described in which the LALI-core mechanism is placed in a growing geometric framework with predifferentiated "apical," differentiating "active," and irreversibly differentiated "frozen" zones defined by distance from an apical source of a fibroblast growth factor (FGF)-type morphogen. This model is shown to account for classic features of the developing limb, including the proximodistal (PD) emergence over time of increasing numbers of bones. We review earlier and recent work suggesting that the inhibitory component of the LALI system for condensation may not be a diffusible morphogen, and propose an alternative mechanism for lateral inhibition, based on synchronization of oscillations of a Hes mediator of the Notch signaling pathway. Finally, we discuss how viewing development as an interplay between molecular-genetic and dynamic physical processes can provide new insight into the origin of congenital anomalies.

Drosophila melanogaster and the development of biology in the 20th century

The fruit fly Drosophila has played a central role in the development of biology during the 20th century. First chosen as a convenient organism to test evolutionary theories soon became the central element in an elaborate, fruitful, and insightful research program dealing with the nature and function of the gene. Through the activities of TH Morgan and his students, Drosophila did more than any other organism to lay down the foundations of genetics as a discipline and a tool for biology. In the last third of the century, a judicious blend of classical genetics and molecular biology focused on some mutants affecting the pattern of the Drosophila larva and the adult, and unlocked the molecular mechanisms of development. Surprisingly, many of the genes identified in this exercise turned to be conserved across organisms. This observation provided a vista of universality at a fundamental level of biological activity. At the dawn of the 21st century, Drosophila continues to be center stage in the development of biology and to open new ways of seeing cells and to understand the construction and the functioning of organisms.

The Decapentaplegic morphogen gradient: from pattern formation to growth regulation

Morphogens have been linked to numerous developmental processes, including organ patterning and the control of organ size. Here we review how different experimental approaches have led to an unprecedented level of molecular knowledge about the patterning role of the Drosophila melanogaster morphogen Decapentaplegic (DPP, the homologue of vertebrate bone morphogenetic protein, or BMP), the first validated secreted morphogen. In addition, we discuss how little is known about the role of the DPP morphogen in the control of organ growth and organ size. Continued efforts to elucidate the role of DPP in D. melanogaster is likely to shed light on this fundamental question in the near future.

Robustness and stability of the gene regulatory network involved in DV boundary formation in the Drosophila wing

Gene regulatory networks have been conserved during evolution. The Drosophila wing and the vertebrate hindbrain share the gene network involved in the establishment of the boundary between dorsal and ventral compartments in the wing and adjacent rhombomeres in the hindbrain. A positive feedback-loop between boundary and non-boundary cells and mediated by the activities of Notch and Wingless/Wnt-1 leads to the establishment of a Notch dependent organizer at the boundary. By means of a Systems Biology approach that combines mathematical modeling and both in silico and in vivo experiments in the Drosophila wing primordium, we modeled and tested this regulatory network and present evidence that a novel property, namely refractoriness to the Wingless signaling molecule, is required in boundary cells for the formation of a stable dorsal-ventral boundary. This new property has been validated in vivo, promotes mutually exclusive domains of Notch and Wingless activities and confers stability to the dorsal-ventral boundary. A robustness analysis of the regulatory network complements our results and ensures its biological plausibility.

Localized multiphoton photoactivation of paGFP in Drosophila wing imaginal discs

In biological imaging of fluorescent molecules, multiphoton laser scanning microscopy (MPLSM) has become the favorite method of fluorescence microscopy in tissue explants and living animals. The great power of MPLSM with pulsed lasers in the infrared wavelength lies in its relatively deep optical penetration and reduced ability to cause potential nonspecific phototoxicity. These properties are of crucial importance for long time-lapse imaging. Since the excited area is intrinsically confined to the high-intensity focal volume of the illuminating beam, MPLSM can also be applied as a tool for selectively manipulating fluorophores in a known, three-dimensionally defined volume within the tissue. Here we introduce localized multiphoton photoactivation (MP-PA) as a technique suitable for analyzing the dynamics of photoactivated molecules with three-dimensional spatial resolution of a few micrometers. Short, intense laser light pulses uncage photoactivatable molecules via multiphoton excitation in a defined volume. MP-PA is demonstrated on photoactivatable paGFP in Drosophila wing imaginal discs. This technique is especially useful for extracting quantitative information about the properties of photoactivatable fusion proteins in different cellular locations in living tissue as well as to label single or small patches of cells in tissue to track their subsequent lineage.

Dynamic decapentaplegic signaling regulates patterning and adhesion in the Drosophila pupal retina

The correct organization of cells within an epithelium is essential for proper tissue and organ morphogenesis. The role of Decapentaplegic/Bone morphogenetic protein (Dpp/BMP) signaling in cellular morphogenesis during epithelial development is poorly understood. In this paper, we used the developing Drosophila pupal retina--looking specifically at the reorganization of glial-like support cells that lie between the retinal ommatidia--to better understand the role of Dpp signaling during epithelial patterning. Our results indicate that Dpp pathway activity is tightly regulated across time in the pupal retina and that epithelial cells in this tissue require Dpp signaling to achieve their correct shape and position within the ommatidial hexagon. These results point to the Dpp pathway as a third component and functional link between two adhesion systems, Hibris-Roughest and DE-cadherin. A balanced interplay between these three systems is essential for epithelial patterning during morphogenesis of the pupal retina. Importantly, we identify a similar functional connection between Dpp activity and DE-cadherin and Rho1 during cell fate determination in the wing, suggesting a broader link between Dpp function and junctional integrity during epithelial development.

Kinetics of morphogen gradient formation

In the developing fly wing, secreted morphogens such as Decapentaplegic (Dpp) and Wingless (Wg) form gradients of concentration providing positional information. Dpp forms a longer-range gradient than Wg. To understand how the range is controlled, we measured the four key kinetic parameters governing morphogen spreading: the production rate, the effective diffusion coefficient, the degradation rate, and the immobile fraction. The four parameters had different values for Dpp versus Wg. In addition, Dynamin-dependent endocytosis was required for spreading of Dpp, but not Wg. Thus, the cellular mechanisms of Dpp and Wingless spreading are different: Dpp spreading requires endocytic, intracellular trafficking.