Kinetics of morphogen gradient formation

Dynamics of morphogen source formation in a growing tissue

A tight regulation of morphogen production is key for morphogen gradient formation and thereby for reproducible and organised organ development. Although many genetic interactions involved in the establishment of morphogen production domains are known, the biophysical mechanisms of morphogen source formation are poorly understood. Here we addressed this by focusing on the morphogen Sonic hedgehog (Shh) in the vertebrate neural tube. Shh is produced by the adjacently located notochord and by the floor plate of the neural tube. Using a data-constrained computational screen, we identified different possible mechanisms by which floor plate formation can occur, only one of which is consistent with experimental data. In this mechanism, the floor plate is established rapidly in response to Shh from the notochord and the dynamics of regulatory interactions within the neural tube. In this process, uniform activators and Shh-dependent repressors are key for establishing the floor plate size. Subsequently, the floor plate becomes insensitive to Shh and increases in size due to tissue growth, leading to scaling of the floor plate with neural tube size. In turn, this results in scaling of the Shh amplitude with tissue growth. Thus, this mechanism ensures a separation of time scales in floor plate formation, so that the floor plate domain becomes growth-dependent after an initial rapid establishment phase. Our study raises the possibility that the time scale separation between specification and growth might be a common strategy for scaling the morphogen gradient amplitude in growing organs. The model that we developed provides a new opportunity for quantitative studies of morphogen source formation in growing tissues.

Loss of the ability to regenerate body appendages in vertebrates: from side effects of evolutionary innovations to gene loss

The ability to regenerate large body appendages is an ancestral trait of vertebrates, which varies across different animal groups. While anamniotes (fish and amphibians) commonly possess this ability, it is notably restricted in amniotes (reptiles, birds, and mammals). In this review, we explore the factors contributing to the loss of regenerative capabilities in amniotes. First, we analyse the potential negative impacts on appendage regeneration caused by four evolutionary innovations: advanced immunity, skin keratinization, whole-body endothermy, and increased body size. These innovations emerged as amniotes transitioned to terrestrial habitats and were correlated with a decline in regeneration capability. Second, we examine the role played by the loss of regeneration-related enhancers and genes initiated by these innovations in the fixation of an inability to regenerate body appendages at the genomic level. We propose that following the cessation of regenerative capacity, the loss of highly specific regeneration enhancers could represent an evolutionarily neutral event. Consequently, the loss of such enhancers might promptly follow the suppression of regeneration as a side effect of evolutionary innovations. By contrast, the loss of regeneration-related genes, due to their pleiotropic functions, would only take place if such loss was accompanied by additional evolutionary innovations that compensated for the loss of pleiotropic functions unrelated to regeneration, which would remain even after participation of these genes in regeneration was lost. Through a review of the literature, we provide evidence that, in many cases, the loss in amniotes of genes associated with body appendage regeneration in anamniotes was significantly delayed relative to the time when regenerative capability was lost. We hypothesise that this delay may be attributed to the necessity for evolutionary restructuring of developmental mechanisms to create conditions where the loss of these genes was a beneficial innovation for the organism. Experimental investigation of the downregulation of genes involved in the regeneration of body appendages in anamniotes but absent in amniotes offers a promising avenue to uncover evolutionary innovations that emerged from the loss of these genes. We propose that the vast majority of regeneration-related genes lost in amniotes (about 150 in humans) may be involved in regulating the early stages of limb and tail regeneration in anamniotes. Disruption of this stage, rather than the late stage, may not interfere with the mechanisms of limb and tail bud development during embryogenesis, as these mechanisms share similarities with those operating in the late stage of regeneration. Consequently, the most promising approach to restoring regeneration in humans may involve creating analogs of embryonic limb buds using stem cell-based tissue-engineering methods, followed by their transfer to the amputation stump. Due to the loss of many genes required specifically during the early stage of regeneration, this approach may be more effective than attempting to induce both early and late stages of regeneration directly in the stump itself.

DNA microbeads for spatio-temporally controlled morphogen release within organoids

Organoids are transformative in vitro model systems that mimic features of the corresponding tissue in vivo. However, across tissue types and species, organoids still often fail to reach full maturity and function because biochemical cues cannot be provided from within the organoid to guide their development. Here we introduce nanoengineered DNA microbeads with tissue mimetic tunable stiffness for implementing spatio-temporally controlled morphogen gradients inside of organoids at any point in their development. Using medaka retinal organoids and early embryos, we show that DNA microbeads can be integrated into embryos and organoids by microinjection and erased in a non-invasive manner with light. Coupling a recombinant surrogate Wnt to the DNA microbeads, we demonstrate the spatio-temporally controlled morphogen release from the microinjection site, which leads to morphogen gradients resulting in the formation of retinal pigmented epithelium while maintaining neuroretinal cell types. Thus, we bioengineered retinal organoids to more closely mirror the cell type diversity of in vivo retinae. Owing to the facile, one-pot fabrication process, the DNA microbead technology can be adapted to other organoid systems for improved tissue mimicry.

The evolution of developmental biology through conceptual and technological revolutions

Developmental biology-the study of the processes by which cells, tissues, and organisms develop and change over time-has entered a new golden age. After the molecular genetics revolution in the 80s and 90s and the diversification of the field in the early 21st century, we have entered a phase when powerful technologies provide new approaches and open unexplored avenues. Progress in the field has been accelerated by advances in genomics, imaging, engineering, and computational biology and by emerging model systems ranging from tardigrades to organoids. We summarize how revolutionary technologies have led to remarkable progress in understanding animal development. We describe how classic questions in gene regulation, pattern formation, morphogenesis, organogenesis, and stem cell biology are being revisited. We discuss the connections of development with evolution, self-organization, metabolism, time, and ecology. We speculate how developmental biology might evolve in an era of synthetic biology, artificial intelligence, and human engineering.

Heparan sulfate-dependent phase separation of CCL5 and its chemotactic activity

Secreted chemokines form concentration gradients in target tissues to control migratory directions and patterns of immune cells in response to inflammatory stimulation; however, how the gradients are formed is much debated. Heparan sulfate (HS) binds to chemokines and modulates their activities. In this study, we investigated the roles of HS in the gradient formation and chemoattractant activity of CCL5 that is known to bind to HS. CCL5 and heparin underwent liquid-liquid phase separation and formed gradient, which was confirmed using CCL5 immobilized on heparin-beads. The biological implication of HS in CCL5 gradient formation was established in CHO-K1 (wild-type) and CHO-677 (lacking HS) cells by Transwell assay. The effect of HS on CCL5 chemoattractant activity was further proved by Transwell assay of human peripheral blood cells. Finally, peritoneal injection of the chemokines into mice showed reduced recruitment of inflammatory cells either by mutant CCL5 (lacking heparin-binding sequence) or by addition of heparin to wild-type CCL5. Our experimental data propose that co-phase separation of CCL5 with HS establishes a specific chemokine concentration gradient to trigger directional cell migration. The results warrant further investigation on other heparin-binding chemokines and allows for a more elaborate insight into disease process and new treatment strategies.

The Clock and Wavefront Self-Organizing model recreates the dynamics of mouse somitogenesis in vivo and in vitro

During mouse development, presomitic mesoderm cells synchronize Wnt and Notch oscillations, creating sequential phase waves that pattern somites. Traditional somitogenesis models attribute phase waves to a global modulation of the oscillation frequency. However, increasing evidence suggests that they could arise in a self-organizing manner. Here, we introduce the Sevilletor, a novel reaction-diffusion system that serves as a framework to compare different somitogenesis patterning hypotheses. Using this framework, we propose the Clock and Wavefront Self-Organizing model that considers an excitable self-organizing region where phase waves form independent of global frequency gradients. The model recapitulates the change in relative phase of Wnt and Notch observed during mouse somitogenesis and provides a theoretical basis for understanding the excitability of mouse presomitic mesoderm cells in vitro.

Transfer of polarity information via diffusion of Wnt ligands in C. elegans embryos

Different signaling mechanisms concur to ensure robust tissue patterning and cell fate instruction during animal development. Most of these mechanisms rely on signaling proteins that are produced, transported, and detected. The spatiotemporal dynamics of signaling molecules are largely unknown, yet they determine signal activity's spatial range and time frame. Here, we use the Caenorhabditis elegans embryo to study how Wnt ligands, an evolutionarily conserved family of signaling proteins, dynamically organize to establish cell polarity in a developing tissue. We identify how Wnt ligands, produced in the posterior half of the embryos, spread extracellularly to transmit information to distant target cells in the anterior half. With quantitative live imaging and fluorescence correlation spectroscopy, we show that Wnt ligands diffuse through the embryo over a timescale shorter than the cell cycle, in the intercellular space, and outside the tissue below the eggshell. We extracted diffusion coefficients of Wnt ligands and their receptor Frizzled and characterized their co-localization. Integrating our different measurements and observations in a simple computational framework, we show how fast diffusion in the embryo can polarize individual cells through a time integration of the arrival of the ligands at the target cells. The polarity established at the tissue level by a posterior Wnt source can be transferred to the cellular level. Our results support a diffusion-based long-range Wnt signaling, which is consistent with the dynamics of developing processes.

Understanding and manipulating extracellular behaviors of Wnt ligands

Wnt, a family of secreted signaling proteins, serves diverse functions in embryogenesis, organogenesis, cancer, and stem cell functions. In the context of development, Wnt has been considered a representative morphogen, forming concentration gradients to give positional information to cells or tissues. However, although gradients are often illustrated in schemata, the reality of concentration gradients, or in other words, actual spatial distribution of Wnt ligands, and their behaviors in the extracellular space still remain poorly known. To understand extracellular behavior of Wnt ligands, quantitative analyses such as fluorescence correlation spectroscopy (FCS) and fluorescence recovery after photobleaching (FRAP) are highly informative because Wnt dispersal involves physical and biochemical processes, such as diffusion and binding to or dissociation from cell surface molecules, including heparan sulfate proteoglycans (HSPGs). Here, I briefly discuss representative methods to quantify morphogen dynamics. In addition, I discuss molecular manipulations of morphogens, mainly focusing on use of protein binders, and synthetic biology of morphogens as indicators of current and future directions in this field.

Long-range formation of the Bicoid gradient requires multiple dynamic modes that spatially vary across the embryo

Morphogen gradients provide essential positional information to gene networks through their spatially heterogeneous distribution, yet how they form is still hotly contested, with multiple models proposed for different systems. Here, we focus on the transcription factor Bicoid (Bcd), a morphogen that forms an exponential gradient across the anterior-posterior (AP) axis of the early Drosophila embryo. Using fluorescence correlation spectroscopy we find there are spatial differences in Bcd diffusivity along the AP axis, with Bcd diffusing more rapidly in the posterior. We establish that such spatially varying differences in Bcd dynamics are sufficient to explain how Bcd can have a steep exponential gradient in the anterior half of the embryo and yet still have an observable fraction of Bcd near the posterior pole. In the nucleus, we demonstrate that Bcd dynamics are impacted by binding to DNA. Addition of the Bcd homeodomain to eGFP::NLS qualitatively replicates the Bcd concentration profile, suggesting this domain regulates Bcd dynamics. Our results reveal how a long-range gradient can form while retaining a steep profile through much of its range.

Dally is not essential for Dpp spreading or internalization but for Dpp stability by antagonizing Tkv-mediated Dpp internalization

Dpp/BMP acts as a morphogen to provide positional information in the Drosophila wing disc. Key cell-surface molecules to control Dpp morphogen gradient formation and signaling are heparan sulfate proteoglycans (HSPGs). In the wing disc, two HSPGs, the glypicans Division abnormally delayed (Dally) and Dally-like (Dlp) have been suggested to act redundantly to control these processes through direct interaction of their heparan sulfate (HS) chains with Dpp. Based on this assumption, a number of models on how glypicans control Dpp gradient formation and signaling have been proposed, including facilitating or hindering Dpp spreading, stabilizing Dpp on the cell surface, or recycling Dpp. However, how distinct HSPGs act remains largely unknown. Here, we generate genome-engineering platforms for the two glypicans and find that only Dally is critical for Dpp gradient formation and signaling through interaction of its core protein with Dpp. We also find that this interaction is not sufficient and that the HS chains of Dally are essential for these functions largely without interacting with Dpp. We provide evidence that the HS chains of Dally are not essential for spreading or recycling of Dpp but for stabilizing Dpp on the cell surface by antagonizing receptor-mediated Dpp internalization. These results provide new insights into how distinct HSPGs control morphogen gradient formation and signaling during development.

Quantitative Live Imaging of Zebrafish Scale Regeneration: From Adult Fish to Signaling Patterns and Tissue Flows

In regeneration, a damaged body part grows back to its original form. Understanding the mechanisms and physical principles underlying this process has been limited by the difficulties of visualizing cell signals and behaviors in regeneration. Zebrafish scales are emerging as a model system to investigate morphogenesis during vertebrate regeneration using quantitative live imaging. Scales are millimeter-sized dermal bone disks forming a skeletal armor on the body of the fish. The scale bone is deposited by an adjacent monolayer of osteoblasts that, after scale loss, regenerates in about 2 weeks. This intriguing regenerative process is accessible to live confocal microscopy, quantifications, and mathematical modeling. Here, I describe methods to image scale regeneration live, tissue-wide and at sub-cellular resolution. Furthermore, I describe methods to process the resulting images and quantify cell, tissue, and signal dynamics.

Geometric effects position renal vesicles during kidney development

During kidney development, reciprocal signaling between the epithelium and the mesenchyme coordinates nephrogenesis with branching morphogenesis of the collecting ducts. The mechanism that positions the renal vesicles, and thus the nephrons, relative to the branching ureteric buds has remained elusive. By combining computational modeling and experiments, we show that geometric effects concentrate the key regulator, WNT9b, at the junctions between parent and daughter branches where renal vesicles emerge, even when uniformly expressed in the ureteric epithelium. This curvature effect might be a general paradigm to create non-uniform signaling in development.

2D effects enhance precision of gradient-based tissue patterning

Robust embryonic development requires pattern formation with high spatial accuracy. In epithelial tissues that are patterned by morphogen gradients, the emerging patterns achieve levels of precision that have recently been explained by a simple one-dimensional reaction-diffusion model with kinetic noise. Here, we show that patterning precision is even greater if transverse diffusion effects are at play in such tissues. The positional error, a measure for spatial patterning accuracy, decreases in wider tissues but then saturates beyond a width of about ten cells. This demonstrates that the precision of gradient-based patterning in two- or higher-dimensional systems can be even greater than predicted by 1D models, and further attests to the potential of noisy morphogen gradients for high-precision tissue patterning.

The Drosophila blood-brain barrier regulates sleep via Moody G protein-coupled receptor signaling

Sleep is vital for most animals, yet its mechanism and function remain unclear. We found that permeability of the BBB (blood-brain barrier)-the organ required for the maintenance of homeostatic levels of nutrients, ions, and other molecules in the brain-is modulated by sleep deprivation (SD) and can cell-autonomously effect sleep changes. We observed increased BBB permeability in known sleep mutants as well as in acutely sleep-deprived animals. In addition to molecular tracers, SD-induced BBB changes also increased the penetration of drugs used in the treatment of brain pathologies. After chronic/genetic or acute SD, rebound sleep or administration of the sleeping aid gaboxadol normalized BBB permeability, showing that SD effects on the BBB are reversible. Along with BBB permeability, RNA levels of the BBB master regulator moody are modulated by sleep. Conversely, altering BBB permeability alone through glia-specific modulation of moody, gαo, loco, lachesin, or neuroglian-each a well-studied regulator of BBB function-was sufficient to induce robust sleep phenotypes. These studies demonstrate a tight link between BBB permeability and sleep and indicate a unique role for the BBB in the regulation of sleep.

The Interaction of Mechanics and the Hippo Pathway in Drosophila melanogaster

Drosophila melanogaster has emerged as an ideal system for studying the networks that control tissue development and homeostasis and, given the similarity of the pathways involved, controlled and uncontrolled growth in mammalian systems. The signaling pathways used in patterning the Drosophila wing disc are well known and result in the emergence of interaction of these pathways with the Hippo signaling pathway, which plays a central role in controlling cell proliferation and apoptosis. Mechanical effects are another major factor in the control of growth, but far less is known about how they exert their control. Herein, we develop a mathematical model that integrates the mechanical interactions between cells, which occur via adherens and tight junctions, with the intracellular actin network and the Hippo pathway so as to better understand cell-autonomous and non-autonomous control of growth in response to mechanical forces.

Is Drosophila Dpp/BMP morphogen spreading required for wing patterning and growth?

Secreted signaling molecules act as morphogens to control patterning and growth in many developing tissues. Since locally produced morphogens spread to form a concentration gradient in the surrounding tissue, spreading is generally thought to be the key step in the non-autonomous actions. Here, we review recent advances in tool development to investigate morphogen function using the role of decapentaplegic (Dpp)/bone morphogenetic protein (BMP)-type ligand in the Drosophila wing disc as an example. By applying protein binder tools to distinguish between the roles of Dpp spreading and local Dpp signaling, we found that Dpp signaling in the source cells is important for wing patterning and growth but Dpp spreading from this source cells is not as strictly required as previously thought. Given recent studies showing unexpected requirements of long-range action of different morphogens, manipulating endogenous morphogen gradients by synthetic protein binder tools could shed more light on how morphogens act in developing tissues.

Reconstitution of morphogen shuttling circuits

Developing tissues form spatial patterns by establishing concentration gradients of diffusible signaling proteins called morphogens. The bone morphogenetic protein (BMP) morphogen pathway uses a family of extracellular modulators to reshape signaling gradients by actively "shuttling" ligands to different locations. It has remained unclear what circuits are sufficient to enable shuttling, what other patterns they can generate, and whether shuttling is evolutionarily conserved. Here, using a synthetic, bottom-up approach, we compared the spatiotemporal dynamics of different extracellular circuits. Three proteins-Chordin, Twsg, and the BMP-1 protease-successfully displaced gradients by shuttling ligands away from the site of production. A mathematical model explained the different spatial dynamics of this and other circuits. Last, combining mammalian and Drosophila components in the same system suggests that shuttling is a conserved capability. Together, these results reveal principles through which extracellular circuits control the spatiotemporal dynamics of morphogen signaling.

Early radial positional information in the cochlea is optimized by a precise linear BMP gradient and enhanced by SOX2

Positional information encoded in signaling molecules is essential for early patterning in the prosensory domain of the developing cochlea. The sensory epithelium, the organ of Corti, contains an exquisite repeating pattern of hair cells and supporting cells. This requires precision in the morphogen signals that set the initial radial compartment boundaries, but this has not been investigated. To measure gradient formation and morphogenetic precision in developing cochlea, we developed a quantitative image analysis procedure measuring SOX2 and pSMAD1/5/9 profiles in mouse embryos at embryonic day (E)12.5, E13.5, and E14.5. Intriguingly, we found that the pSMAD1/5/9 profile forms a linear gradient up to the medial ~ 75% of the PSD from the pSMAD1/5/9 peak in the lateral edge during E12.5 and E13.5. This is a surprising activity readout for a diffusive BMP4 ligand secreted from a tightly constrained lateral region since morphogens typically form exponential or power-law gradient shapes. This is meaningful for gradient interpretation because while linear profiles offer the theoretically highest information content and distributed precision for patterning, a linear morphogen gradient has not yet been observed. Furthermore, this is unique to the cochlear epithelium as the pSMAD1/5/9 gradient is exponential in the surrounding mesenchyme. In addition to the information-optimized linear profile, we found that while pSMAD1/5/9 is stable during this timeframe, an accompanying gradient of SOX2 shifts dynamically. Last, through joint decoding maps of pSMAD1/5/9 and SOX2, we see that there is a high-fidelity mapping between signaling activity and position in the regions that will become Kölliker's organ and the organ of Corti. Mapping is ambiguous in the prosensory domain precursory to the outer sulcus. Altogether, this research provides new insights into the precision of early morphogenetic patterning cues in the radial cochlea prosensory domain.

The impact of cell size on morphogen gradient precision

Tissue patterning during embryonic development is remarkably precise. Here, we numerically determine the impact of the cell diameter, gradient length and the morphogen source on the variability of morphogen gradients. We show that the positional error increases with the gradient length relative to the size of the morphogen source, and with the square root of the cell diameter and the readout position. We provide theoretical explanations for these relationships, and show that they enable high patterning precision over developmental time for readouts that scale with expanding tissue domains, as observed in the Drosophila wing disc. Our analysis suggests that epithelial tissues generally achieve higher patterning precision with small cross-sectional cell areas. An extensive survey of measured apical cell areas shows that they are indeed small in developing tissues that are patterned by morphogen gradients. Enhanced precision may thus have led to the emergence of pseudostratification in epithelia, a phenomenon for which the evolutionary benefit had so far remained elusive.

Patterning precision under non-linear morphogen decay and molecular noise

Morphogen gradients can instruct cells about their position in a patterned tissue. Non-linear morphogen decay has been suggested to increase gradient precision by reducing the sensitivity to variability in the morphogen source. Here, we use cell-based simulations to quantitatively compare the positional error of gradients for linear and non-linear morphogen decay. While we confirm that non-linear decay reduces the positional error close to the source, the reduction is very small for physiological noise levels. Far from the source, the positional error is much larger for non-linear decay in tissues that pose a flux barrier to the morphogen at the boundary. In light of this new data, a physiological role of morphogen decay dynamics in patterning precision appears unlikely.

Gradient to sectioning CUBE workflow for the generation and imaging of organoids with localized differentiation

Advancements in organoid culture have led to various in vitro mini-organs that mimic native tissues in many ways. Yet, the bottleneck remains to generate complex organoids with body axis patterning, as well as keeping the orientation of organoids during post-experiment analysis processes. Here, we present a workflow for culturing organoids with morphogen gradient using a CUBE culture device, followed by sectioning samples with the CUBE to retain information on gradient direction. We show that hiPSC spheroids cultured with two separated differentiation media on opposing ends of the CUBE resulted in localized expressions of the respective differentiation markers, in contrast to homogeneous distribution of markers in controls. We also describe the processes for cryo and paraffin sectioning of spheroids in CUBE to retain gradient orientation information. This workflow from gradient culture to sectioning with CUBE can provide researchers with a convenient tool to generate increasingly complex organoids and study their developmental processes in vitro.

Cellular compartmentalisation and receptor promiscuity as a strategy for accurate and robust inference of position during morphogenesis

Precise spatial patterning of cell fate during morphogenesis requires accurate inference of cellular position. In making such inferences from morphogen profiles, cells must contend with inherent stochasticity in morphogen production, transport, sensing and signalling. Motivated by the multitude of signalling mechanisms in various developmental contexts, we show how cells may utilise multiple tiers of processing (compartmentalisation) and parallel branches (multiple receptor types), together with feedback control, to bring about fidelity in morphogenetic decoding of their positions within a developing tissue. By simultaneously deploying specific and nonspecific receptors, cells achieve a more accurate and robust inference. We explore these ideas in the patterning of Drosophila melanogaster wing imaginal disc by Wingless morphogen signalling, where multiple endocytic pathways participate in decoding the morphogen gradient. The geometry of the inference landscape in the high dimensional space of parameters provides a measure for robustness and delineates stiff and sloppy directions. This distributed information processing at the scale of the cell highlights how local cell autonomous control facilitates global tissue scale design.

Stability of Pattern Formation in Systems with Dynamic Source Regions

We explain the principles of gene expression pattern stabilization in systems of interacting, diffusible morphogens, with dynamically established source regions. Using a reaction-diffusion model with a step-function production term, we identify the phase transition between low-precision indeterminate patterning and the phase in which a traveling, well-defined contact zone between two domains is formed. Our model analytically explains single- and two-gene domain dynamics and provides pattern stability conditions for all possible two-gene regulatory network motifs.

Precision of morphogen-driven tissue patterning during development is enhanced through contact-mediated cellular interactions

Cells in developing embryos reliably differentiate to attain location-specific fates, despite fluctuations in morphogen concentrations that provide positional information and in molecular processes that interpret it. We show that local contact-mediated cell-cell interactions utilize inherent asymmetry in the response of patterning genes to the global morphogen signal yielding a bimodal response. This results in robust developmental outcomes with a consistent identity for the dominant gene at each cell, substantially reducing the uncertainty in the location of boundaries between distinct fates.

Single-molecule tracking of Nodal and Lefty in live zebrafish embryos supports hindered diffusion model

The hindered diffusion model postulates that the movement of a signaling molecule through an embryo is affected by tissue geometry and binding-mediated hindrance, but these effects have not been directly demonstrated in vivo. Here, we visualize extracellular movement and binding of individual molecules of the activator-inhibitor signaling pair Nodal and Lefty in live developing zebrafish embryos using reflected light-sheet microscopy. We observe that diffusion coefficients of molecules are high in extracellular cavities, whereas mobility is reduced and bound fractions are high within cell-cell interfaces. Counterintuitively, molecules nevertheless accumulate in cavities, which we attribute to the geometry of the extracellular space by agent-based simulations. We further find that Nodal has a larger bound fraction than Lefty and shows a binding time of tens of seconds. Together, our measurements and simulations provide direct support for the hindered diffusion model and yield insights into the nanometer-to-micrometer-scale mechanisms that lead to macroscopic signal dispersal.

Patterning principles of morphogen gradients

Metazoan embryos develop from a single cell into three-dimensional structured organisms while groups of genetically identical cells attain specialized identities. Cells of the developing embryo both create and accurately interpret morphogen gradients to determine their positions and make specific decisions in response. Here, we first cover intellectual roots of morphogen and positional information concepts. Focusing on animal embryos, we then provide a review of current understanding on how morphogen gradients are established and how their spans are controlled. Lastly, we cover how gradients evolve in time and space during development, and how they encode information to control patterning. In sum, we provide a list of patterning principles for morphogen gradients and review recent advances in quantitative methodologies elucidating information provided by morphogens.

Long-range morphogen gradient formation by cell-to-cell signal propagation

Morphogen gradients are a central concept in developmental biology. Their formation often involves the secretion of morphogens from a local source, that spread by diffusion in the cell field, where molecules eventually get degraded. This implies limits to both the time and length scales over which morphogen gradients can form which are set by diffusion coefficients and degradation rates. Towards the goal of identifying plausible mechanisms capable of extending the gradient range, we here use theory to explore properties of a cell-to-cell signaling relay. Inspired by the millimeter-scale Wnt-expression and signaling gradients in flatworms, we consider morphogen-mediated morphogen production in the cell field. We show that such a relay can generate stable morphogen and signaling gradients that are oriented by a local, morphogen-independent source of morphogen at a boundary. This gradient formation can be related to an effective diffusion and an effective degradation that result from morphogen production due to signaling relay. If the secretion of morphogen produced in response to the relay is polarized, it further gives rise to an effective drift. We find that signaling relay can generate long-ranged gradients in relevant times without relying on extreme choices of diffusion coefficients or degradation rates, thus exceeding the limits set by physiological diffusion coefficients and degradation rates. A signaling relay is hence an attractive principle to conceptualize long-range gradient formation by slowly diffusing morphogens that are relevant for patterning in adult contexts such as regeneration and tissue turn-over.

Localization of signaling receptors maximizes cellular information acquisition in spatially structured natural environments

Cells in natural environments, such as tissue or soil, sense and respond to extracellular ligands with intricately structured and non-monotonic spatial distributions, sculpted by processes such as fluid flow and substrate adhesion. In this work, we show that spatial sensing and navigation can be optimized by adapting the spatial organization of signaling pathways to the spatial structure of the environment. We develop an information-theoretic framework for computing the optimal spatial organization of a sensing system for a given signaling environment. We find that receptor localization previously observed in cells maximizes information acquisition in simulated natural contexts, including tissue and soil. Specifically, information acquisition is maximized when receptors form localized patches at regions of maximal ligand concentration. Receptor localization extends naturally to produce a dynamic protocol for continuously redistributing signaling receptors, which when implemented using simple feedback, boosts cell navigation efficiency by 30-fold.

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.

Regulatory mechanisms of cytoneme-based morphogen transport

During development and tissue homeostasis, cells must communicate with their neighbors to ensure coordinated responses to instructional cues. Cues such as morphogens and growth factors signal at both short and long ranges in temporal- and tissue-specific manners to guide cell fate determination, provide positional information, and to activate growth and survival responses. The precise mechanisms by which such signals traverse the extracellular environment to ensure reliable delivery to their intended cellular targets are not yet clear. One model for how this occurs suggests that specialized filopodia called cytonemes extend between signal-producing and -receiving cells to function as membrane-bound highways along which information flows. A growing body of evidence supports a crucial role for cytonemes in cell-to-cell communication. Despite this, the molecular mechanisms by which cytonemes are initiated, how they grow, and how they deliver specific signals are only starting to be revealed. Herein, we discuss recent advances toward improved understanding of cytoneme biology. We discuss similarities and differences between cytonemes and other types of cellular extensions, summarize what is known about how they originate, and discuss molecular mechanisms by which their activity may be controlled in development and tissue homeostasis. We conclude by highlighting important open questions regarding cytoneme biology, and comment on how a clear understanding of their function may provide opportunities for treating or preventing disease.

Size matters: tissue size as a marker for a transition between reaction-diffusion regimes in spatio-temporal distribution of morphogens

The reaction-diffusion model constitutes one of the most influential mathematical models to study distribution of morphogens in tissues. Despite its widespread use, the effect of finite tissue size on model-predicted spatio-temporal morphogen distributions has not been completely elucidated. In this study, we analytically investigated the spatio-temporal distributions of morphogens predicted by a reaction-diffusion model in a finite one-dimensional domain, as a proxy for a biological tissue, and compared it with the solution of the infinite-domain model. We explored the reduced parameter, the tissue length in units of a characteristic reaction-diffusion length, and identified two reaction-diffusion regimes separated by a crossover tissue size estimated in approximately three characteristic reaction-diffusion lengths. While above this crossover the infinite-domain model constitutes a good approximation, it breaks below this crossover, whereas the finite-domain model faithfully describes the entire parameter space. We evaluated whether the infinite-domain model renders accurate estimations of diffusion coefficients when fitted to finite spatial profiles, a procedure typically followed in fluorescence recovery after photobleaching (FRAP) experiments. We found that the infinite-domain model overestimates diffusion coefficients when the domain is smaller than the crossover tissue size. Thus, the crossover tissue size may be instrumental in selecting the suitable reaction-diffusion model to study tissue morphogenesis.

Morphogen gradient scaling by recycling of intracellular Dpp

Morphogen gradients are fundamental to establish morphological patterns in developing tissues¹. During development, gradients scale to remain proportional to the size of growing organs^2,3. Scaling is a universal gear adjusting patterns to size in living organisms^3-8, yet its mechanisms remain unclear. Here, focusing on the Dpp gradient in the Drosophila wing disc, we unravel a cell biological basis behind scaling. From small to large discs, scaling of the Dpp gradient is achieved by increasing the contribution of the internalized Dpp molecules to Dpp transport: to expand the gradient, endocytosed molecules are re-exocytosed to spread extracellularly. To regulate the contribution of endocytosed Dpp to the spreading extracellular pool during tissue growth, it is the Dpp binding rates that are progressively modulated by the extracellular factor Pentagone, driving scaling. Thus, for some morphogens, evolution may act on endocytic trafficking to regulate the range of the gradient and its scaling, which could allow adaptation of shape and pattern to different sizes of organs in different species.

Targeted search for scaling genes reveals matrixmetalloproteinase 3 as a scaler of the dorsal-ventral pattern in Xenopus laevis embryos

How embryos scale patterning according to size is still not fully understood. Through in silico screening and analysis of reaction-diffusion systems that could be responsible for scaling, we predicted the existence of genes whose expression is sensitive to embryo size and which regulate the scaling of embryonic patterning. To find these scalers, we identified genes with strongly altered expression in half-size Xenopus laevis embryos compared with full-size siblings at the gastrula stage. Among found genes, we investigated the role of matrix metalloproteinase-3 (mmp3), which was most strongly downregulated in half-size embryos. We show that Mmp3 scales dorsal-ventral patterning by degrading the slowly diffusing embryonic inducers Noggin1 and Noggin2 but preventing cleavage of the more rapidly diffusing inducer Chordin via degradation of a Tolloid-type proteinase. In addition to unraveling the mechanism underlying the scaling of dorsal-ventral patterning, this work provides proof of principal for scalers identification in embryos of other species.

Using FCS to accurately measure protein concentration in the presence of noise and photobleaching

Quantitative cell biology requires precise and accurate concentration measurements, resolved both in space and time. Fluorescence correlation spectroscopy (FCS) has been held as a promising technique to perform such measurements because the fluorescence fluctuations it relies on are directly dependent on the absolute number of fluorophores in the detection volume. However, the most interesting applications are in cells, where autofluorescence and confinement result in strong background noise and important levels of photobleaching. Both noise and photobleaching introduce systematic bias in FCS concentration measurements and need to be corrected for. Here, we propose to make use of the photobleaching inevitably occurring in confined environments to perform series of FCS measurements at different fluorophore concentration, which we show allows a precise in situ measurement of both background noise and molecular brightness. Such a measurement can then be used as a calibration to transform confocal intensity images into concentration maps. The power of this approach is first illustrated with in vitro measurements using different dye solutions, then its applicability for in vivo measurements is demonstrated in Drosophila embryos for a model nuclear protein and for two morphogens, Bicoid and Capicua.

Pegasus, a small extracellular peptide enhancing short-range diffusion of Wingless

Small Open Reading Frames (smORFs) coding for peptides of less than 100 amino-acids are an enigmatic and pervasive gene class, found in the tens of thousands in metazoan genomes. Here we reveal a short 80 amino-acid peptide (Pegasus) which enhances Wingless/Wnt1 protein short-range diffusion and signalling. During Drosophila wing development, Wingless has sequential functions, including late induction of proneural gene expression and wing margin development. Pegasus mutants produce wing margin defects and proneural expression loss similar to those of Wingless. Pegasus is secreted, and co-localizes and co-immunoprecipitates with Wingless, suggesting their physical interaction. Finally, measurements of fixed and in-vivo Wingless gradients support that Pegasus increases Wingless diffusion in order to enhance its signalling. Our results unveil a new element in Wingless signalling and clarify the patterning role of Wingless diffusion, while corroborating the link between small open reading frame peptides, and regulation of known proteins with membrane-related functions.

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.

Tissue hydraulics: Physics of lumen formation and interaction

Lumen formation plays an essential role in the morphogenesis of tissues during development. Here we review the physical principles that play a role in the growth and coarsening of lumens. Solute pumping by the cell, hydraulic flows driven by differences of osmotic and hydrostatic pressures, balance of forces between extracellular fluids and cell-generated cytoskeletal forces, and electro-osmotic effects have been implicated in determining the dynamics and steady-state of lumens. We use the framework of linear irreversible thermodynamics to discuss the relevant force, time and length scales involved in these processes. We focus on order of magnitude estimates of physical parameters controlling lumen formation and coarsening.

A Random Walk Approach to Transport in Tissues and Complex Media: From Microscale Descriptions to Macroscale Models

The biological processes necessary for the development and continued survival of any organism are often strongly influenced by the transport properties of various biologically active species. The transport phenomena involved vary over multiple temporal and spatial scales, from organism-level behaviors such as the search for food, to systemic processes such as the transport of oxygen from the lungs to distant organs, down to microscopic phenomena such as the stochastic movement of proteins in a cell. Each of these processes is influenced by many interrelated factors. Identifying which factors are the most important, and how they interact to determine the overall result is a problem of great importance and interest. Experimental observations are often fit to relatively simple models, but in reality the observations are the output of complicated functions of the physicochemical, topological, and geometrical properties of a given system. Herein we use multistate continuous-time random walks and generalized master equations to model transport processes involving spatial jumps, immobilization at defined sites, and stochastic internal state changes. The underlying spatial models, which are framed as graphs, may have different classes of nodes, and walkers may have internal states that are governed by a Markov process. A general form of the solutions, using Fourier-Laplace transforms and asymptotic analysis, is developed for several spatially infinite regular lattices in one and two spatial dimensions, and the theory is developed for the analysis of transport and internal state changes on general graphs. The goal in each case is to shed light on how experimentally observable macroscale transport coefficients can be explained in terms of microscale properties of the underlying processes. This work is motivated by problems arising in transport in biological tissues, but the results are applicable to a broad class of problems that arise in other applications.

The pattern of nodal morphogen signaling is shaped by co-receptor expression

Embryos must communicate instructions to their constituent cells over long distances. These instructions are often encoded in the concentration of signals called morphogens. In the textbook view, morphogen molecules diffuse from a localized source to form a concentration gradient, and target cells adopt fates by measuring the local morphogen concentration. However, natural patterning systems often incorporate numerous co-factors and extensive signaling feedback, suggesting that embryos require additional mechanisms to generate signaling patterns. Here, we examine the mechanisms of signaling pattern formation for the mesendoderm inducer Nodal during zebrafish embryogenesis. We find that Nodal signaling activity spans a normal range in the absence of signaling feedback and relay, suggesting that diffusion is sufficient for Nodal gradient formation. We further show that the range of endogenous Nodal ligands is set by the EGF-CFC co-receptor Oep: in the absence of Oep, Nodal activity spreads to form a nearly uniform distribution throughout the embryo. In turn, increasing Oep levels sensitizes cells to Nodal ligands. We recapitulate these experimental results with a computational model in which Oep regulates the diffusive spread of Nodal ligands by setting the rate of capture by target cells. This model predicts, and we confirm in vivo, the surprising observation that a failure to replenish Oep transforms the Nodal signaling gradient into a travelling wave. These results reveal that patterns of Nodal morphogen signaling are shaped by co-receptor-mediated restriction of ligand spread and sensitization of responding cells.

Quantitative analyses reveal extracellular dynamics of Wnt ligands in Xenopus embryos

The mechanism of intercellular transport of Wnt ligands is still a matter of debate. To better understand this issue, we examined the distribution and dynamics of Wnt8 in Xenopus embryos. While Venus-tagged Wnt8 was found on the surfaces of cells close to Wnt-producing cells, we also detected its dispersal over distances of 15 cell diameters. A combination of fluorescence correlation spectroscopy and quantitative imaging suggested that only a small proportion of Wnt8 ligands diffuses freely, whereas most Wnt8 molecules are bound to cell surfaces. Fluorescence decay after photoconversion showed that Wnt8 ligands bound on cell surfaces decrease exponentially, suggesting a dynamic exchange of bound forms of Wnt ligands. Mathematical modeling based on this exchange recapitulates a graded distribution of bound, but not free, Wnt ligands. Based on these results, we propose that Wnt distribution in tissues is controlled by a dynamic exchange of its abundant bound and rare free populations.

Roadmap for the multiscale coupling of biochemical and mechanical signals during development

The way in which interactions between mechanics and biochemistry lead to the emergence of complex cell and tissue organization is an old question that has recently attracted renewed interest from biologists, physicists, mathematicians and computer scientists. Rapid advances in optical physics, microscopy and computational image analysis have greatly enhanced our ability to observe and quantify spatiotemporal patterns of signalling, force generation, deformation, and flow in living cells and tissues. Powerful new tools for genetic, biophysical and optogenetic manipulation are allowing us to perturb the underlying machinery that generates these patterns in increasingly sophisticated ways. Rapid advances in theory and computing have made it possible to construct predictive models that describe how cell and tissue organization and dynamics emerge from the local coupling of biochemistry and mechanics. Together, these advances have opened up a wealth of new opportunities to explore how mechanochemical patterning shapes organismal development. In this roadmap, we present a series of forward-looking case studies on mechanochemical patterning in development, written by scientists working at the interface between the physical and biological sciences, and covering a wide range of spatial and temporal scales, organisms, and modes of development. Together, these contributions highlight the many ways in which the dynamic coupling of mechanics and biochemistry shapes biological dynamics: from mechanoenzymes that sense force to tune their activity and motor output, to collectives of cells in tissues that flow and redistribute biochemical signals during development.

Diversity and robustness of bone morphogenetic protein pattern formation

Pattern formation by bone morphogenetic proteins (BMPs) demonstrates remarkable plasticity and utility in several contexts, such as early embryonic development, tissue patterning and the maintenance of stem cell niches. BMPs pattern tissues over many temporal and spatial scales: BMP gradients as short as 1-2 cell diameters maintain the stem cell niche of the Drosophila germarium over a 24-h cycle, and BMP gradients of several hundred microns establish dorsal-ventral tissue specification in Drosophila, zebrafish and Xenopus embryos in timescales between 30 min and several hours. The mechanisms that shape BMP signaling gradients are also incredibly diverse. Although ligand diffusion plays a dominant role in forming the gradient, a cast of diffusible and non-diffusible regulators modulate gradient formation and confer robustness, including scale invariance and adaptability to perturbations in gene expression and growth. In this Review, we document the diverse ways that BMP gradients are formed and refined, and we identify the core principles that they share to achieve reliable performance.

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.

Wavelength of a Turing-type mechanism regulates the morphogenesis of meshwork patterns

The meshwork pattern is a significant pattern in the development of biological tissues and organs. It is necessary to explore the mathematical mechanism of meshwork pattern formation. In this paper, we found that the meshwork pattern is formed by four kinds of stalk behaviours: stalk extension, tip bifurcation, side branching and tip fusion. The Turing-type pattern underlying the meshwork pattern is a Turing spot pattern, which indicates that the Turing instability of the spot pattern promotes activator peak formation and then guides the formation of meshwork patterns. Then, we found that the Turing wavelength decreased in turn from tip bifurcation to side branching to tip fusion via statistical evaluation. Through the functional relationship between the Turing wavelength and model parameters ([Formula: see text] and [Formula: see text]), we found that parameters [Formula: see text] and [Formula: see text] had monotonic effects on the Turing wavelength and that parameter [Formula: see text] had nonmonotonic effects. Furthermore, we performed simulations of local meshwork pattern formation under variable model parameter values. The simulation results verified the corresponding relationship between the Turing wavelength and stalk behaviours and the functional relationship between the Turing wavelength and model parameters. The simulation results showed that the Turing wavelength regulated the meshwork pattern and that the small Turing wavelength facilitated dense meshwork pattern formation. Our work provides novel insight into and understanding of the formation of meshwork patterns. We believe that studies associated with network morphogenesis can benefit from our work.

Global constraints within the developmental program of the Drosophila wing

Organismal development is a complex process, involving a vast number of molecular constituents interacting on multiple spatio-temporal scales in the formation of intricate body structures. Despite this complexity, development is remarkably reproducible and displays tolerance to both genetic and environmental perturbations. This robustness implies the existence of hidden simplicities in developmental programs. Here, using the Drosophila wing as a model system, we develop a new quantitative strategy that enables a robust description of biologically salient phenotypic variation. Analyzing natural phenotypic variation across a highly outbred population and variation generated by weak perturbations in genetic and environmental conditions, we observe a highly constrained set of wing phenotypes. Remarkably, the phenotypic variants can be described by a single integrated mode that corresponds to a non-intuitive combination of structural variations across the wing. This work demonstrates the presence of constraints that funnel environmental inputs and genetic variation into phenotypes stretched along a single axis in morphological space. Our results provide quantitative insights into the nature of robustness in complex forms while yet accommodating the potential for evolutionary variations. Methodologically, we introduce a general strategy for finding such invariances in other developmental contexts.

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.

Interpretation of morphogen gradients by a synthetic bistable circuit

During development, cells gain positional information through the interpretation of dynamic morphogen gradients. A proposed mechanism for interpreting opposing morphogen gradients is mutual inhibition of downstream transcription factors, but isolating the role of this specific motif within a natural network remains a challenge. Here, we engineer a synthetic morphogen-induced mutual inhibition circuit in E. coli populations and show that mutual inhibition alone is sufficient to produce stable domains of gene expression in response to dynamic morphogen gradients, provided the spatial average of the morphogens falls within the region of bistability at the single cell level. When we add sender devices, the resulting patterning circuit produces theoretically predicted self-organised gene expression domains in response to a single gradient. We develop computational models of our synthetic circuits parameterised to timecourse fluorescence data, providing both a theoretical and experimental framework for engineering morphogen-induced spatial patterning in cell populations.

Morphogen gradients can be dynamic and transient yet give rise to stable cellular patterns. Here the authors show that a synthetic morphogen-induced mutual inhibition circuit produces stable boundaries when the spatial average of morphogens falls within the region of bistability.