Organism-scale modeling of early Drosophila patterning via bone morphogenetic proteins

Bone morphogenetic protein signaling: the pathway and its regulation

In the mid-1960s, bone morphogenetic proteins (BMPs) were first identified in the extracts of bone to have the remarkable ability to induce heterotopic bone. When the Drosophila gene decapentaplegic (dpp) was first identified to share sequence similarity with mammalian BMP2/BMP4 in the late-1980s, it became clear that secreted BMP ligands can mediate processes other than bone formation. Following this discovery, collaborative efforts between Drosophila geneticists and mammalian biochemists made use of the strengths of their respective model systems to identify BMP signaling components and delineate the pathway. The ability to conduct genetic modifier screens in Drosophila with relative ease was critical in identifying the intracellular signal transducers for BMP signaling and the related transforming growth factor-beta/activin signaling pathway. Such screens also revealed a host of genes that encode other core signaling components and regulators of the pathway. In this review, we provide a historical account of this exciting time of gene discovery and discuss how the field has advanced over the past 30 years. We have learned that while the core BMP pathway is quite simple, composed of 3 components (ligand, receptor, and signal transducer), behind the versatility of this pathway lies multiple layers of regulation that ensures precise tissue-specific signaling output. We provide a sampling of these discoveries and highlight many questions that remain to be answered to fully understand the complexity of BMP signaling.

The nested embryonic dorsal domains of BMP-target genes are not scaled to size during the evolution of Drosophila species

Egg size is a fast-evolving trait among Drosophilids expected to change the spatial distribution of morphogens that pattern the embryonic axes. Here we asked whether the patterning of the dorsal region of the embryo by the Decapentaplegic/Bone Morphogenetic Protein-4 (DPP/BMP-4) gradient is scaled among Drosophila species with different egg sizes. This region specifies the extra-embryonic tissue amnioserosa and the ectoderm. We find that the entire dorsal region scales with embryo size, but the gene expression patterns regulated by DPP are not proportional, suggesting that the DPP gradient is differentially scaled during evolution. To further test whether the DPP gradient can scale or not in Drosophila melanogaster, we created embryos with expanded dorsal regions that mimic changes in scale seen in other species and measured the resulting domains of DPP-target genes. We find that the proportions of these domains are not maintained, suggesting that the DPP gradient is unable to scale in the embryo. These and previous findings suggest that the embryonic dorso-ventral patterning lack scaling in the ventral and dorsal sides but is robust in the lateral region where the neuroectoderm is specified and two opposing gradients, Dorsal/NFkappa-B and DPP, intersect. We propose that the lack of scaling of the DPP gradient may contribute to changes in the size of the amnioserosa and the numbers of ectodermal cells with specific cortical tensions, which are expected to generate distinct mechanical forces for gastrulating embryos of different sizes.

Modelling the structure of Short Gastrulation and generation of a toolkit for studying its function in Drosophila

A BMP gradient is essential for patterning the dorsal-ventral axis of invertebrate and vertebrate embryos. The extracellular BMP binding protein Short Gastrulation (Sog) in Drosophila plays a key role in BMP gradient formation. In this study, we combine genome editing, structural and developmental approaches to study Sog function in Drosophila. We generate a sog knockout fly stock, which allows simple reintegration of altered versions of the sog coding sequence. As proof-of-principle, we test the requirement for two cysteine residues that were previously identified as targets for palmitoylation, which has been proposed to enhance Sog secretion. However, we show that the sogC27,28S mutant is viable with only very mild phenotypes, indicating that these residues and their potential modification are not critical for Sog secretion in vivo. Additionally, we use experimental negative stain EM imaging and hydrodynamic data to validate the AlphaFold structure prediction for Sog. The model suggests a more compact shape than the vertebrate ortholog Chordin and conformational flexibility between the C-terminal von Willebrand C domains. We discuss how this altered compactness may contribute to mechanistic differences in Sog and Chordin function during BMP gradient formation. This article has an associated First Person interview with the first author of the paper.

The developing wing crossvein of Drosophila melanogaster: a fascinating model for signaling and morphogenesis

The Drosophila wing has been used as a model for studying tissue growth, morphogenesis and pattern formation. The wing veins of Drosophila are composed of two distinct structures, longitudinal veins and crossveins. Although positional information of longitudinal veins is largely defined in the wing imaginal disc during the larval stage, crossvein primordial cells appear to be naive until the early pupal stage. Here, we first review how wing crossveins have been investigated in the past. Then, the developmental mechanisms underlying crossvein formation are summarized. This review focuses on how a conserved trafficking mechanism of BMP ligands is utilized for crossvein formation, and how various co-factors play roles in sustaining BMP signalling. Recent findings further reveal that crossvein development serves as an excellent model to address how BMP signal and dynamic cellular processes are coupled. This comprehensive review illustrates the uniqueness, scientific value and future perspectives of wing crossvein development as a model.

Scalable inference of transcriptional kinetic parameters from MS2 time series data

MOTIVATION

The MS2-MCP (MS2 coat protein) live imaging system allows for visualization of transcription dynamics through the introduction of hairpin stem-loop sequences into a gene. A fluorescent signal at the site of nascent transcription in the nucleus quantifies mRNA production. Computational modelling can be used to infer the promoter states along with the kinetic parameters governing transcription, such as promoter switching frequency and polymerase loading rate. However, modelling of the fluorescent trace presents a challenge due its persistence; the observed fluorescence at a given time point depends on both current and previous promoter states. A compound state Hidden Markov Model (cpHMM) was recently introduced to allow inference of promoter activity from MS2-MCP data. However, the computational time for inference scales exponentially with gene length and the cpHMM is therefore not currently practical for application to many eukaryotic genes.

RESULTS

We present a scalable implementation of the cpHMM for fast inference of promoter activity and transcriptional kinetic parameters. This new method can model genes of arbitrary length through the use of a time-adaptive truncated compound state space. The truncated state space provides a good approximation to the full state space by retaining the most likely set of states at each time during the forward pass of the algorithm. Testing on MS2-MCP fluorescent data collected from early Drosophila melanogaster embryos indicates that the method provides accurate inference of kinetic parameters within a computationally feasible timeframe. The inferred promoter traces generated by the model can also be used to infer single-cell transcriptional parameters.

AVAILABILITY AND IMPLEMENTATION

Python implementation is available at https://github.com/ManchesterBioinference/burstInfer, along with code to reproduce the examples presented here.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Heterodimer-heterotetramer formation mediates enhanced sensor activity in a biophysical model for BMP signaling

Numerous stages of organismal development rely on the cellular interpretation of gradients of secreted morphogens including members of the Bone Morphogenetic Protein (BMP) family through transmembrane receptors. Early gradients of BMPs drive dorsal/ventral patterning throughout the animal kingdom in both vertebrates and invertebrates. Growing evidence in Drosophila, zebrafish, murine and other systems suggests that BMP ligand heterodimers are the primary BMP signaling ligand, even in systems in which mixtures of BMP homodimers and heterodimers are present. Signaling by heterodimers occurs through a hetero-tetrameric receptor complex comprising of two distinct type one BMP receptors and two type II receptors. To understand the system dynamics and determine whether kinetic assembly of heterodimer-heterotetramer BMP complexes is favored, as compared to other plausible BMP ligand-receptor configurations, we developed a kinetic model for BMP tetramer formation based on current measurements for binding rates and affinities. We find that contrary to a common hypothesis, heterodimer-heterotetramer formation is not kinetically favored over the formation of homodimer-tetramer complexes under physiological conditions of receptor and ligand concentrations and therefore other mechanisms, potentially including differential kinase activities of the formed heterotetramer complexes, must be the cause of heterodimer-heterotetramer signaling primacy. Further, although BMP complex assembly favors homodimer and homomeric complex formation over a wide range of parameters, ignoring these signals and instead relying on the heterodimer improves the range of morphogen interpretation in a broad set of conditions, suggesting a performance advantage for heterodimer signaling in patterning multiple cell types in a gradient.

TGF-β signaling is an important cell signaling system through which cells respond to external information. In the TGF-β system, signaling is initiated when a ligand dimer pair binds to a receptor tetramer. Interestingly, in numerous developmental contexts, TGF-β signaling has a greater response to heterodimeric ligands (dimers of multiple ligands), as compared to homomeric ligands (dimers made of two molecules of a single ligand). However, neither the cause of heterodimer signaling primacy, nor the systemic effects of heterodimeric vs homomeric signaling are understood. We use a biophysically-informed computational modeling approach to investigate the system dynamics of heterodimer-heterotetramer BMP signaling, to understand the cause and consequence of the requirement for Bmp2/7-mediated signaling in dorsoventral patterning in zebrafish development. Using our model, we demonstrate that BMP heterodimer signaling complex formation is not kinetically favored over homodimer signaling complexes, suggesting subfunctionalization of BMP receptors may be required to explain heterodimer signaling. Additionally, we show that heterodimer signaling provides a performance advantage via increased range of morphogen interpretation. Our findings provide insight into the systems principles involved in developmental signaling.

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.

Evaluation of BMP-mediated patterning in a 3D mathematical model of the zebrafish blastula embryo

Bone Morphogenetic Proteins (BMPs) play an important role in dorsal-ventral (DV) patterning of the early zebrafish embryo. BMP signaling is regulated by a network of extracellular and intracellular factors that impact the range and signaling of BMP ligands. Recent advances in understanding the mechanism of pattern formation support a source-sink mechanism, however it is not clear how the source-sink mechanism shapes patterns in 3D, nor how sensitive the pattern is to biophysical rates and boundary conditions along both the anteroposterior (AP) and DV axes of the embryo. We propose a new three-dimensional growing Partial Differential Equation (PDE)-based model to simulate the BMP patterning process during the blastula stage. This model provides a starting point to elucidate how different mechanisms and components work together in 3D to create and maintain the BMP gradient in the embryo. We also show how the 3D model fits the BMP signaling gradient data at multiple time points along both axes. Furthermore, sensitivity analysis of the model suggests that the spatiotemporal patterns of Chordin and BMP ligand gene expression are dominant drivers of shape in 3D and more work is needed to quantify the spatiotemporal profiles of gene and protein expression to further refine the models.

Coacting enhancers can have complementary functions within gene regulatory networks and promote canalization

Developmental genes are often regulated by multiple enhancers exhibiting similar spatiotemporal outputs, which are generally considered redundantly acting though few have been studied functionally. Using CRISPR-Cas9, we created deletions of two enhancers, brk5' and brk3', that drive similar but not identical expression of the gene brinker (brk) in early Drosophila embryos. Utilizing both in situ hybridization and quantitative mRNA analysis, we investigated the changes in the gene network state caused by the removal of one or both of the early acting enhancers. brk5' deletion generally phenocopied the gene mutant, including expansion of the BMP ligand decapentaplegic (dpp) as well as inducing variability in amnioserosa tissue cell number suggesting a loss of canalization. In contrast, brk3' deletion presented unique phenotypes including dorsal expansion of several ventrally expressed genes and a decrease in amnioserosa cell number. Similarly, deletions were made for two enhancers associated with the gene short-gastrulation (sog), sog.int and sog.dist, demonstrating that they also exhibit distinct patterning phenotypes and affect canalization. In summary, this study shows that similar gene expression driven by coacting enhancers can support distinct, and sometimes complementary, functions within gene regulatory networks and, moreover, that phenotypes associated with individual enhancer deletion mutants can provide insight into new gene functions.

Scale invariance of BMP signaling gradients in zebrafish

In both vertebrates and invertebrates, spatial patterning along the Dorsal-ventral (DV) embryonic axis depends on a morphogen gradient of Bone Morphogenetic Protein signaling. Scale invariance of DV patterning by BMPs has been found in both vertebrates and invertebrates, however the mechanisms that regulate gradient scaling remain controversial. To obtain quantitative data that can be used to address core questions of scaling, we introduce a method to tune the size of zebrafish embryos by reducing varying amounts of vegetal yolk. We quantified the BMP signaling gradient in wild-type and perturbed embryos and found that the system scales for reductions in cross-sectional perimeter of up to 30%. Furthermore, we found that the degree of scaling for intraspecies scaling within zebrafish is greater than that between Danioninae species.

Imaging and Quantification of P-Smad1/5 in Zebrafish Blastula and Gastrula Embryos

Spatiotemporal patterns of morphogen activity drive differential gene expression with a high degree of precision within a developing embryo and reproducibly between embryos. Understanding the formation and function of a morphogen gradient during development requires quantitative measurement of morphogen activity throughout an individual embryo and also between embryos within a population. Quantification of morphogen gradients in to presents unique challenges in imaging and image processing to minimize error and maximize the quality of the data so it may be used in computational models of development and in statistically testing hypotheses. Here we present methods for the preparation, immunostaining, imaging, and quantification of a bone morphogenetic protein (BMP) activity gradient in individual zebrafish embryos as well as methods for acquiring population-level statistics after embryo grouping and alignment. This quantitative approach can be extended to other morphogen systems, and the computational codes can be adapted to other imaging contexts in zebrafish and other organisms.

Critical Point in Self-Organized Tissue Growth

We present a theory of pattern formation in growing domains inspired by biological examples of tissue development. Gradients of signaling molecules regulate growth, while growth changes these graded chemical patterns by dilution and advection. We identify a critical point of this feedback dynamics, which is characterized by spatially homogeneous growth and proportional scaling of patterns with tissue length. We apply this theory to the biological model system of the developing wing of the fruit fly Drosophila melanogaster and quantitatively identify signatures of the critical point.

Wavenumber selection via spatial parameter jump

The Swift-Hohenberg equation describes an instability which forms finite-wavenumber patterns near onset. We study this equation posed with a spatial inhomogeneity; a jump-type parameter that renders the zero solution stable for x<0 and unstable for x>0. Using normal forms and spatial dynamics, we prove the existence of a family of steady-state solutions that represent a transition in space from a homogeneous state to a striped pattern state. The wavenumbers of these stripes are contained in a narrow band whose width grows linearly with the size of the jump. This represents a severe restriction from the usual constant-parameter case, where the allowed band grows with the square root of the parameter. We corroborate our predictions using numerical continuation and illustrate implications on stability of growing patterns in direct simulations.This article is part of the theme issue 'Stability of nonlinear waves and patterns and related topics'.

Memory functions reveal structural properties of gene regulatory networks

Gene regulatory networks (GRNs) control cellular function and decision making during tissue development and homeostasis. Mathematical tools based on dynamical systems theory are often used to model these networks, but the size and complexity of these models mean that their behaviour is not always intuitive and the underlying mechanisms can be difficult to decipher. For this reason, methods that simplify and aid exploration of complex networks are necessary. To this end we develop a broadly applicable form of the Zwanzig-Mori projection. By first converting a thermodynamic state ensemble model of gene regulation into mass action reactions we derive a general method that produces a set of time evolution equations for a subset of components of a network. The influence of the rest of the network, the bulk, is captured by memory functions that describe how the subnetwork reacts to its own past state via components in the bulk. These memory functions provide probes of near-steady state dynamics, revealing information not easily accessible otherwise. We illustrate the method on a simple cross-repressive transcriptional motif to show that memory functions not only simplify the analysis of the subnetwork but also have a natural interpretation. We then apply the approach to a GRN from the vertebrate neural tube, a well characterised developmental transcriptional network composed of four interacting transcription factors. The memory functions reveal the function of specific links within the neural tube network and identify features of the regulatory structure that specifically increase the robustness of the network to initial conditions. Taken together, the study provides evidence that Zwanzig-Mori projections offer powerful and effective tools for simplifying and exploring the behaviour of GRNs.

Gene regulatory networks are essential for cell fate specification and function. But the recursive links that comprise these networks often make determining their properties and behaviour complicated. Computational models of these networks can also be difficult to decipher. To reduce the complexity of such models we employ a Zwanzig-Mori projection approach. This allows a system of ordinary differential equations, representing a network, to be reduced to an arbitrary subnetwork consisting of part of the initial network, with the rest of the network (bulk) captured by memory functions. These memory functions account for the bulk by describing signals that return to the subnetwork after some time, having passed through the bulk. We show how this approach can be used to simplify analysis and to probe the behaviour of a gene regulatory network. Applying the method to a transcriptional network in the vertebrate neural tube reveals previously unappreciated properties of the network. By taking advantage of the structure of the memory functions we identify interactions within the network that are unnecessary for sustaining correct patterning. Upon further investigation we find that these interactions are important for conferring robustness to variation in initial conditions. Taken together we demonstrate the validity and applicability of the Zwanzig-Mori projection approach to gene regulatory networks.

TGF-β Family Signaling in Drosophila

The transforming growth factor β (TGF-β) family signaling pathway is conserved and ubiquitous in animals. In Drosophila, fewer representatives of each signaling component are present compared with vertebrates, simplifying mechanistic study of the pathway. Although there are fewer family members, the TGF-β family pathway still regulates multiple and diverse functions in Drosophila. In this review, we focus our attention on several of the classic and best-studied functions for TGF-β family signaling in regulating Drosophila developmental processes such as embryonic and imaginal disc patterning, but we also describe several recently discovered roles in regulating hormonal, physiological, neuronal, innate immunity, and tissue homeostatic processes.

Generation of animal form by the Chordin/Tolloid/BMP gradient: 100 years after D'Arcy Thompson

The classic book "On Growth and Form" by naturalist D'Arcy Thompson was published 100 years ago. To celebrate this landmark, we present experiments in the Xenopus embryo that provide a framework for understanding how simple, quantitative transformations of a morphogen gradient might have affected evolution and morphological diversity of organisms. D'Arcy Thompson proposed that different morphologies might be generated by modifying physical parameters in an underlying system of Cartesian coordinates that pre-existed in Nature and arose during evolutionary history. Chordin is a BMP antagonist secreted by the Spemann organizer located on the dorsal side of the gastrula. Chordin generates a morphogen gradient as first proposed by mathematician Alan Turing. The rate-limiting step of this dorsal-ventral (D-V) morphogen is the degradation of Chordin by the Tolloid metalloproteinase in the ventral side. Chordin is expressed at gastrula on the dorsal side where BMP signaling is low, while at the opposite side peak levels of BMP signaling are reached. In fishes, amphibians, reptiles and birds, high BMP signaling in the ventral region induces transcription of a secreted inhibitor of Tolloid called Sizzled. By depleting Sizzled exclusively in the ventral half of the embryo we were able to expand the ventro-posterior region in an otherwise normal embryo. Conversely, ventral depletion of Tolloid, which stabilizes Chordin, decreased ventral and tail structures, phenocopying the tolloid zebrafish mutation. We explain how historical constraints recorded in the language of DNA become subject to the universal laws of physics when an ancestral reaction-diffusion morphogen gradient dictates form.

Systems biology derived source-sink mechanism of BMP gradient formation

A morphogen gradient of Bone Morphogenetic Protein (BMP) signaling patterns the dorsoventral embryonic axis of vertebrates and invertebrates. The prevailing view in vertebrates for BMP gradient formation is through a counter-gradient of BMP antagonists, often along with ligand shuttling to generate peak signaling levels. To delineate the mechanism in zebrafish, we precisely quantified the BMP activity gradient in wild-type and mutant embryos and combined these data with a mathematical model-based computational screen to test hypotheses for gradient formation. Our analysis ruled out a BMP shuttling mechanism and a bmp transcriptionally-informed gradient mechanism. Surprisingly, rather than supporting a counter-gradient mechanism, our analyses support a fourth model, a source-sink mechanism, which relies on a restricted BMP antagonist distribution acting as a sink that drives BMP flux dorsally and gradient formation. We measured Bmp2 diffusion and found that it supports the source-sink model, suggesting a new mechanism to shape BMP gradients during development.

Before an animal is born, a protein called BMP plays a key role in establishing the difference between the front and the back of the animal. Cells nearer the front of the embryo contain higher amounts of the BMP protein, whilst cells nearer the back have progressively lower levels of BMP. This gradient of BMP ‘concentration’ affects the identity of the cells, with the level of BMP in each cell dictating what parts of the body are made where.

The prevailing view among scientists is that the BMP gradient is created by an opposing gradient of another protein called Chordin, which is found at high levels at the back of the embryo and lower levels near the front. Chordin inhibits BMP and the interaction between the two proteins establishes the gradients that create order across the embryo.

Zinski et al. used computer models to investigate how the BMP gradient is created. Several possibilities were considered, including the effect of Chordin. Comparing the models to precise experimental measurements of BMP activity in zebrafish embryos suggested that a different mechanism known as a source-sink model, rather than the opposing Chordin gradient, may be responsible for the pattern of BMP found in the embryo. In this model, the BMP is produced at the front of the embryo and moves towards the back end by diffusion. At the back of the embryo, BMP is mopped up by Chordin, resulting in a constant gradient of BMP along the embryo.

Many other processes that control how animals grow and develop rely on the formation of similar protein gradients, so these findings may also apply to other aspects of animal development. Understanding how animals grow and develop may help researchers to develop strategies to regrow tissues and organs in human patients.

Control of signaling molecule range during developmental patterning

Tissue patterning, through the concerted activity of a small number of signaling pathways, is critical to embryonic development. While patterning can involve signaling between neighbouring cells, in other contexts signals act over greater distances by traversing complex cellular landscapes to instruct the fate of distant cells. In this review, we explore different strategies adopted by cells to modulate signaling molecule range to allow correct patterning. We describe mechanisms for restricting signaling range and highlight how such short-range signaling can be exploited to not only control the fate of adjacent cells, but also to generate graded signaling within a field of cells. Other strategies include modulation of signaling molecule action by tissue architectural properties and the use of cellular membranous structures, such as signaling filopodia and exosomes, to actively deliver signaling ligands to target cells. Signaling filopodia can also be deployed to reach out and collect particular signals, thereby precisely controlling their site of action.

Systems Health: A Transition from Disease Management Toward Health Promotion

To date, most of the chronic diseases such as cancer, cardiovascular disease, and diabetes, are the leading cause of death. Current strategies toward disease treatment, e.g., risk prediction and target therapy, still have limitations for precision medicine due to the dynamic and complex nature of health. Interactions among genetics, lifestyle, and surrounding environments have nonnegligible effects on disease evolution. Thus a transition in health-care area is urgently needed to address the hysteresis of diagnosis and stabilize the increasing health-care costs. In this chapter, we explored new insights in the field of health promotion and introduced the integration of systems theories with health science and clinical practice. On the basis of systems biology and systems medicine, a novel concept called "systems health" was comprehensively advocated. Two types of bioinformatics models, i.e., causal loop diagram and quantitative model, were selected as examples for further illumination. Translational applications of these models in systems health were sequentially discussed. Moreover, we highlighted the bridging of ancient and modern views toward health and put forward a proposition for citizen science and citizen empowerment in health promotion.

lolal Is an Evolutionarily New Epigenetic Regulator of dpp Transcription during Dorsal-Ventral Axis Formation

Secreted ligands in the Dpp/BMP family drive dorsal–ventral (D/V) axis formation in all Bilaterian species. However, maternal factors regulating Dpp/BMP transcription in this process are largely unknown. We identified the BTB domain protein longitudinals lacking-like (lolal) as a modifier of decapentaplegic (dpp) mutations. We show that Lolal is evolutionarily related to the Trithorax group of chromatin regulators and that lolal interacts genetically with the epigenetic factor Trithorax-like during Dpp D/V signaling. Maternally driven Lolal^HA is found in oocytes and translocates to zygotic nuclei prior to the point at which dpp transcription begins. lolal maternal and zygotic mutant embryos display significant reductions in dpp, pMad, and zerknullt expression, but they are never absent. The data suggest that lolal is required to maintain dpp transcription during D/V patterning. Phylogenetic data revealed that lolal is an evolutionarily new gene present only in insects and crustaceans. We conclude that Lolal is the first maternal protein identified with a role in dpp D/V transcriptional maintenance, that Lolal and the epigenetic protein Trithorax-like are essential for Dpp D/V signaling and that the architecture of the Dpp D/V pathway evolved in the arthropod lineage after the separation from vertebrates via the incorporation of new genes such as lolal.

Maternal AP determinants in the Drosophila oocyte and embryo

An animal embryo cannot initiate its journey of forming a new life on its own. It must rely on maternally provided resources and inputs to kick-start its developmental process. In Drosophila, the initial polarities of the embryo along both the anterior-posterior (AP) and dorsal-ventral (DV) axes are also specified by maternal determinants. Over the past several decades, genetic and molecular studies have identified and characterized such determinants, as well as the zygotic genetic regulatory networks that control patterning in the early embryo. Extensive studies of oogenesis have also led to a detailed knowledge of the cellular and molecular interactions that control the formation of a mature egg. Despite these efforts, oogenesis and embryogenesis have been studied largely as separate problems, except for qualitative aspects with regard to maternal regulation of the asymmetric localization of maternal determinants. Can oogenesis and embryogenesis be viewed from a unified perspective at a quantitative level, and can that improve our understanding of how robust embryonic patterning is achieved? Here, we discuss the basic knowledge of the regulatory mechanisms controlling oogenesis and embryonic patterning along the AP axis. We explore properties of the maternal Bicoid gradient in relation to embryo size in search for a unified framework for robust AP patterning. WIREs Dev Biol 2016, 5:562-581. doi: 10.1002/wdev.235 For further resources related to this article, please visit the WIREs website.

Sequential construction of a model for modular gene expression control, applied to spatial patterning of theDrosophilagenehunchback

Gene network simulations are increasingly used to quantify mutual gene regulation in biological tissues. These are generally based on linear interactions between single-entity regulatory and target genes. Biological genes, by contrast, commonly have multiple, partially independent, cis-regulatory modules (CRMs) for regulator binding, and can produce variant transcription and translation products. We present a modeling framework to address some of the gene regulatory dynamics implied by this biological complexity. Spatial patterning of the hunchback (hb) gene in Drosophila development involves control by three CRMs producing two distinct mRNA transcripts. We use this example to develop a differential equations model for transcription which takes into account the cis-regulatory architecture of the gene. Potential regulatory interactions are screened by a genetic algorithms (GAs) approach and compared to biological expression data.

Visualizing retinoic acid morphogen gradients

Morphogens were originally defined as secreted signaling molecules that diffuse from local sources to form concentration gradients, which specify multiple cell fates. More recently morphogen gradients have been shown to incorporate a range of mechanisms including short-range signal activation, transcriptional/translational feedback, and temporal windows of target gene induction. Many critical cell-cell signals implicated in both embryonic development and disease, such as Wnt, fibroblast growth factor (Fgf), hedgehog (Hh), transforming growth factor beta (TGFb), and retinoic acid (RA), are thought to act as morphogens, but key information on signal propagation and ligand distribution has been lacking for most. The zebrafish provides unique advantages for genetics and imaging to address gradients during early embryonic stages when morphogens help establish major body axes. This has been particularly informative for RA, where RA response elements (RAREs) driving fluorescent reporters as well as Fluorescence Resonance Energy Transfer (FRET) reporters of receptor binding have provided evidence for gradients, as well as regulatory mechanisms that attenuate noise and enhance gradient robustness in vivo. Here we summarize available tools in zebrafish and discuss their utility for studying dynamic regulation of RA morphogen gradients, through combined experimental and computational approaches.

Peak BMP Responses in the Drosophila Embryo Are Dependent on the Activation of Integrin Signaling

Within a 3D tissue, cells need to integrate signals from growth factors, such as BMPs, and the extracellular matrix (ECM) to coordinate growth and differentiation. Here, we use the Drosophila embryo as a model to investigate how BMP responses are influenced by a cell’s local ECM environment. We show that integrins, which are ECM receptors, are absolutely required for peak BMP signaling. This stimulatory effect of integrins requires their intracellular signaling function, which is activated by the ECM protein collagen IV. Mechanistically, integrins interact with the BMP receptor and stimulate phosphorylation of the downstream Mad transcription factor. The BMP-pathway-enhancing function of integrins is independent of focal adhesion kinase, but it requires conserved NPXY motifs in the β-integrin cytoplasmic tail. Furthermore, we show that an α-integrin subunit is a BMP target gene, identifying positive feedback between integrin signaling and BMP pathway activity that may contribute to robust cell fate decisions.

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Drosophila embryos lacking integrin function have disrupted BMP responses

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Collagen IV activates integrin signaling to enhance levels of the pMad transducer

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Integrins bind BMP receptors and promote pMad levels after BMP receptor activation

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BMP activates expression of an α-integrin, representing a positive feedback loop

Building from the Ground up: Basement Membranes in Drosophila Development

Basement membranes (BMs) are sheetlike extracellular matrices found at the basal surfaces of epithelial tissues. The structural and functional diversity of these matrices within the body endows them with the ability to affect multiple aspects of cell behavior and communication; for this reason, BMs are integral to many developmental processes. The power of Drosophila genetics, as applied to the BM, has yielded substantial insight into how these matrices influence development. Here, we explore three facets of BM biology to which Drosophila research has made particularly important contributions. First, we discuss how newly synthesized BM proteins are secreted to and assembled exclusively on basal epithelial surfaces. Next, we examine how regulation of the structural properties of the BM mechanically supports and guides tissue morphogenesis. Finally, we explore how BMs influence development through the modulation of several major signaling pathways.

Dynamic BMP signaling polarized by Toll patterns the dorsoventral axis in a hemimetabolous insect

Toll-dependent patterning of the dorsoventral axis in Drosophila represents one of the best understood gene regulatory networks. However, its evolutionary origin has remained elusive. Outside the insects Toll is not known for a patterning function, but rather for a role in pathogen defense. Here, we show that in the milkweed bug Oncopeltus fasciatus, whose lineage split from Drosophila's more than 350 million years ago, Toll is only required to polarize a dynamic BMP signaling network. A theoretical model reveals that this network has self-regulatory properties and that shallow Toll signaling gradients are sufficient to initiate axis formation. Such gradients can account for the experimentally observed twinning of insect embryos upon egg fragmentation and might have evolved from a state of uniform Toll activity associated with protecting insect eggs against pathogens.

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

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

zen and the art of phenotypic maintenance: canalization of embryonic dorsal-ventral patterning in Drosophila

We recently uncovered a novel genetic mechanism that generates the phenotypic uniformity, or canalization, of BMP signaling and cell fate specification during patterning of the dorsal-ventral (D/V) axis in D. melanogaster embryos. We went on to show that other wild-type Drosophila species lack this canalizing genetic circuitry and, consequently, have non-robust D/V patterning. In this review, we propose molecular mechanisms that may give rise to stereotyped BMP signaling, and we identify an additional species that could have decanalized D/V patterning. Extension of these analyses could in turn help explain why canalization is not a universal necessity for species survival.

Dynamic scaling of morphogen gradients on growing domains

Developmental mechanisms are highly conserved, yet act in embryos of very different sizes. How scaling is achieved has remained elusive. Here we identify a generally applicable mechanism for dynamic scaling on growing domains and show that it quantitatively agrees with data from the Drosophila wing imaginal disc. We show that for the measured parameter ranges, the Dpp gradient does not reach steady state during Drosophila wing development. We further show that both, pre-steady-state dynamics and advection of cell-bound ligand in a growing tissue can, in principle, enable scaling, even for non-uniform tissue growth. For the parameter values that have been established for the Dpp morphogen in the Drosophila wing imaginal disc, we show that scaling is mainly a result of the pre-steady-state dynamics. Pre-steady-state dynamics are pervasive in morphogen-controlled systems, thus making this a probable general mechanism for dynamic scaling of morphogen gradients in growing developmental systems.

Modeling of the dorsal gradient across species reveals interaction between embryo morphology and Toll signaling pathway during evolution

Morphogenetic gradients are essential to allocate cell fates in embryos of varying sizes within and across closely related species. We previously showed that the maternal NF-κB/Dorsal (Dl) gradient has acquired different shapes in Drosophila species, which result in unequally scaled germ layers along the dorso-ventral axis and the repositioning of the neuroectodermal borders. Here we combined experimentation and mathematical modeling to investigate which factors might have contributed to the fast evolutionary changes of this gradient. To this end, we modified a previously developed model that employs differential equations of the main biochemical interactions of the Toll (Tl) signaling pathway, which regulates Dl nuclear transport. The original model simulations fit well the D. melanogaster wild type, but not mutant conditions. To broaden the applicability of this model and probe evolutionary changes in gradient distributions, we adjusted a set of 19 independent parameters to reproduce three quantified experimental conditions (i.e. Dl levels lowered, nuclear size and density increased or decreased). We next searched for the most relevant parameters that reproduce the species-specific Dl gradients. We show that adjusting parameters relative to morphological traits (i.e. embryo diameter, nuclear size and density) alone is not sufficient to reproduce the species Dl gradients. Since components of the Tl pathway simulated by the model are fast-evolving, we next asked which parameters related to Tl would most effectively reproduce these gradients and identified a particular subset. A sensitivity analysis reveals the existence of nonlinear interactions between the two fast-evolving traits tested above, namely the embryonic morphological changes and Tl pathway components. Our modeling further suggests that distinct Dl gradient shapes observed in closely related melanogaster sub-group lineages may be caused by similar sequence modifications in Tl pathway components, which are in agreement with their phylogenetic relationships.

Embryo size can vary greatly among closely related species. How tissue specification either scales or is modified in the developing embryo in different species is an ongoing investigation in developmental biology. Here we asked how embryo morphology and specific molecular pathways influence tissue specification by altering the distribution of morphogens. Morphogens are molecules that form gradients that regulate gene expression patterns in a dosage-dependent fashion that result in tissue specification, and therefore are a prime target for evolution in order to adjust or maintain tissue proportions in relation to overall embryo size. We used a mathematical model to identify factors that influence the distribution of the Dorsal morphogen gradient that is responsible for patterning the dorsal-ventral axis of the Drosophila fruit fly embryo. We obtained experimental data from mutant conditions and different species of Drosophila to calibrate our model and found an interaction between embryo morphology and regulation of the Toll pathway, which regulates the Dorsal gradient. Furthermore, the model predicts that closely related species share similar modifications in Toll pathway components resulting in their species-specific gradient shapes, which are supported by interspecies amino acid comparison of the components Dorsal and Cactus.

A computational model for BMP movement in sea urchin embryos

Bone morphogen proteins (BMPs) are distributed along a dorsal-ventral (DV) gradient in many developing embryos. The spatial distribution of this signaling ligand is critical for correct DV axis specification. In various species, BMP expression is spatially localized, and BMP gradient formation relies on BMP transport, which in turn requires interactions with the extracellular proteins Short gastrulation/Chordin (Chd) and Twisted gastrulation (Tsg). These binding interactions promote BMP movement and concomitantly inhibit BMP signaling. The protease Tolloid (Tld) cleaves Chd, which releases BMP from the complex and permits it to bind the BMP receptor and signal. In sea urchin embryos, BMP is produced in the ventral ectoderm, but signals in the dorsal ectoderm. The transport of BMP from the ventral ectoderm to the dorsal ectoderm in sea urchin embryos is not understood. Therefore, using information from a series of experiments, we adapt the mathematical model of Mizutani et al. (2005) and embed it as the reaction part of a one-dimensional reaction-diffusion model. We use it to study aspects of this transport process in sea urchin embryos. We demonstrate that the receptor-bound BMP concentration exhibits dorsally centered peaks of the same type as those observed experimentally when the ternary transport complex (Chd-Tsg-BMP) forms relatively quickly and BMP receptor binding is relatively slow. Similarly, dorsally centered peaks are created when the diffusivities of BMP, Chd, and Chd-Tsg are relatively low and that of Chd-Tsg-BMP is relatively high, and the model dynamics also suggest that Tld is a principal regulator of the system. At the end of this paper, we briefly compare the observed dynamics in the sea urchin model to a version that applies to the fly embryo, and we find that the same conditions can account for BMP transport in the two types of embryos only if Tld levels are reduced in sea urchin compared to fly.

Multiscale modeling of dorsoventral patterning in Drosophila

The role of mathematical models of signaling networks is showcased by examples from Drosophila development. Three models of consecutive stages in dorsoventral patterning are presented. We begin with a compartmental model of intracellular reactions that generates a gradient of nuclear-localized Dorsal, exhibiting constant shape and dynamic amplitude. A simple thermodynamic model of equilibrium binding explains how a spatially uniform transcription factor, Zelda, can act in combination with a graded factor, Dorsal, to cooperatively regulate gene expression borders. Finally, we formulate a dynamic and stochastic model that predicts spatiotemporal patterns of Sog expression based on known patterns of its transcription factor, Dorsal. The future of coupling multifarious models across multiple temporal and spatial scales is discussed.

Making models match measurements: model optimization for morphogen patterning networks

Mathematical modeling of developmental signaling networks has played an increasingly important role in the identification of regulatory mechanisms by providing a sandbox for hypothesis testing and experiment design. Whether these models consist of an equation with a few parameters or dozens of equations with hundreds of parameters, a prerequisite to model-based discovery is to bring simulated behavior into agreement with observed data via parameter estimation. These parameters provide insight into the system (e.g., enzymatic rate constants describe enzyme properties). Depending on the nature of the model fit desired - from qualitative (relative spatial positions of phosphorylation) to quantitative (exact agreement of spatial position and concentration of gene products) - different measures of data-model mismatch are used to estimate different parameter values, which contain different levels of usable information and/or uncertainty. To facilitate the adoption of modeling as a tool for discovery alongside other tools such as genetics, immunostaining, and biochemistry, careful consideration needs to be given to how well a model fits the available data, what the optimized parameter values mean in a biological context, and how the uncertainty in model parameters and predictions plays into experiment design. The core discussion herein pertains to the quantification of model-to-data agreement, which constitutes the first measure of a model's performance and future utility to the problem at hand. Integration of this experimental data and the appropriate choice of objective measures of data-model agreement will continue to drive modeling forward as a tool that contributes to experimental discovery. The Drosophila melanogaster gap gene system, in which model parameters are optimized against in situ immunofluorescence intensities, demonstrates the importance of error quantification, which is applicable to a wide array of developmental modeling studies.

Cleavage of the Drosophila screw prodomain is critical for a dynamic BMP morphogen gradient in embryogenesis

Dorsoventral patterning of the Drosophila embryo is regulated by graded distribution of bone morphogenetic proteins (BMPs) composed of two ligands, decapentaplegic (Dpp) a BMP2/4 ortholog and screw (Scw) a BMP5/6/7/8 family member. scw(E1) encodes an unusual allele that was isolated as a dominant enhancer of partial loss-of-function mutations in dpp. However, the molecular mechanisms that underlie this genetic interaction remain to be addressed. Here we show that scw(E1) contains a mutation at the furin cleavage site within the prodomain that is crucial for ligand production. Furthermore, our data show that Scw(E1) preferentially forms heterodimers with Dpp rather than homotypic dimers, providing a possible explanation for the dominant negative phenotype of scw(E1) alleles. The unprocessed prodomain of Scw(E1) remains in a complex with the Dpp:Scw heterodimer, and thus could interfere with interaction of the ligand with the extracellular matrix, or the kinetics of processing/secretion of the ligand in vivo. These data reveal novel mechanisms by which post-translational regulation of Scw can modulate Dpp signaling activity.

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.

A genetic network conferring canalization to a bistable patterning system in Drosophila

To achieve the "constancy of the wild-type," the developing organism must be buffered against stochastic fluctuations and environmental perturbations. This phenotypic buffering has been theorized to arise from a variety of genetic mechanisms and is widely thought to be adaptive and essential for viability. In the Drosophila blastoderm embryo, staining with antibodies against the active, phosphorylated form of the bone morphogenetic protein (BMP) signal transducer Mad, pMad, or visualization of the spatial pattern of BMP-receptor interactions reveals a spatially bistable pattern of BMP signaling centered on the dorsal midline. This signaling event is essential for the specification of dorsal cell fates, including the extraembryonic amnioserosa. BMP signaling is initiated by facilitated extracellular diffusion that localizes BMP ligands dorsally. BMP signaling then activates an intracellular positive feedback circuit that promotes future BMP-receptor interactions. Here, we identify a genetic network comprising three genes that canalizes this BMP signaling event. The BMP target eiger (egr) acts in the positive feedback circuit to promote signaling, while the BMP binding protein encoded by crossveinless-2 (cv-2) antagonizes signaling. Expression of both genes requires the early activity of the homeobox gene zerknüllt (zen). Two Drosophila species lacking early zen expression have high variability in BMP signaling. These data both detail a new mechanism that generates developmental canalization and identify an example of a species with noncanalized axial patterning.

Systems approach to developmental biology--designs for robust patterning

Patterning is an important step in animal development that generates spatially non-uniform gene expression patterns or spatially heterogeneous cellular responses. Patterning is realised by the generation and reading of positional information provided by spatial gradients of morphogens, diffusive chemicals in the extracellular environment. To achieve normal development, accurate patterning that is robust against noise is necessary. Here the authors describe how morphogen gradient formation and gradient interpretation processes are designed to achieve highly reproducible patterning. Furthermore, recent advancements in measurement and imaging techniques have enabled researchers to obtain quantitative dynamic and multi-physical data, not only for chemical events, but also for the geometrical and mechanical properties of cells in vivo. The authors briefly review some recent studies on the effects of such non-chemical events on patterning.

Fine-tuned shuttles for bone morphogenetic proteins

Bone morphogenetic proteins (BMPs) are potent secreted signaling factors that trigger phosphorylation of Smad transcriptional regulators through receptor complex binding at the cell-surface. Resulting changes in target gene expression impact critical cellular responses during development and tissue homeostasis. BMP activity is tightly regulated in time and space by secreted modulators that control BMP extracellular distribution and availability for receptor binding. Such extracellular regulation is key for BMPs to function as morphogens and/or in the formation of morphogen activity gradients. Here, we review shuttling systems utilized to control the distribution of BMP ligands in tissue of various geometries, developing under different temporal constraints. We discuss the biological advantages for employing specific strategies for BMP shuttling and roles of varied ligand forms.

Evaluating thermodynamic models of enhancer activity on cellular resolution gene expression data

With the advent of high throughput sequencing and high resolution transcriptomic technologies, there exists today an unprecedented opportunity to understand gene regulation at a quantitative level. State of the art models of the relationship between regulatory sequence and gene expression have shown great promise, but also suffer from some major shortcomings. In this paper, we identify and address methodological challenges pertaining to quantitative modeling of gene expression from sequence, and test our models on the anterior-posterior patterning system in the Drosophila embryo. We first develop a framework to process cellular resolution three-dimensional gene expression data from the Drosophila embryo and create data sets on which quantitative models can be trained. Next we propose a new score, called 'weighted pattern generating potential' (w-PGP), to evaluate model predictions, and show its advantages over the two most common scoring schemes in use today. The model building exercise uses w-PGP as the evaluation score and adopts a systematic strategy to increase a model's complexity while guarding against over-fitting. Our model identifies three transcription factors--ZELDA, SLOPPY-PAIRED, and NUBBIN--that have not been previously incorporated in quantitative models of this system, as having significant regulatory influence. Finally, we show how fitting quantitative models on data sets comprising a handful of enhancers, as reported in earlier work, may lead to unreliable models.

Creating gradients by morphogen shuttling

Morphogen gradients are used to pattern a field of cells according to variations in the concentration of a signaling molecule. Typically, the morphogen emanates from a confined group of cells. During early embryogenesis, however, the ability to define a restricted source for morphogen production is limited. Thus, various early patterning systems rely on a broadly expressed morphogen that generates an activation gradient within its expression domain. Computational and experimental work has shed light on how a sharp and robust gradient can be established under those situations, leading to a mechanism termed 'morphogen shuttling'. This mechanism relies on an extracellular shuttling molecule that forms an inert, highly diffusible complex with the morphogen. Morphogen release from the complex following cleavage of the shuttling molecule by an extracellular protease leads to the accumulation of free ligand at the center of its expression domain and a graded activation of the developmental pathway that decreases significantly even within the morphogen-expression domain.

Encoding and decoding of positional information in morphogen-dependent patterning

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

The importance of geometry in mathematical models of developing systems

Understanding the interaction between the spatial variation of extracellular signals and the interpretation of such signals in embryonic development is difficult without a mathematical model, but the inherent limitations of a model can have a profound impact on its utility. A central issue is the level of abstraction needed, and here we focus on the role of geometry in models and how the choice of the spatial dimension can influence the conclusions reached. A widely studied system in which the proper choice of geometry is critical is embryonic development of Drosophila melanogaster, and we discuss recent work in which 3D embryo-scale modeling is used to identify key modes of transport, analyze gap gene expression, and test BMP-mediated positive feedback mechanisms.

Image analysis and empirical modeling of gene and protein expression

Protein gradients and gene expression patterns are major determinants in the differentiation and fate map of the developing embryo. Here we discuss computational methods to quantitatively measure the positions of gene expression domains and the gradients of protein expression along the dorsal-ventral axis in the Drosophila embryo. Our methodology involves three layers of data. The first layer, or the primary data, consists of z-stack confocal images of embryos processed by in situ hybridization and/or antibody stainings. The secondary data are relationships between location, usually an x-axis coordinate, and fluorescent intensity of gene or protein detection. Tertiary data comprise the optimal parameters that arise from fits of the secondary data to empirical models. The tertiary data are useful to distill large datasets of imaged embryos down to a tractable number of conceptually useful parameters. This analysis allows us to detect subtle phenotypes and is adaptable to any set of genes or proteins with a canonical pattern. For example, we show how insights into the Dorsal transcription factor protein gradient and its target gene ventral-neuroblasts defective (vnd) were obtained using such quantitative approaches.