Shape and function of the Bicoid morphogen gradient in dipteran species with different sized embryos

Identification of a gene promoter active in Lucilia sericata larval salivary glands using a rapid transient expression assay

Tissue-specific gene promoters are desired as they provide the specificity needed for control of gene expression in transgenic animals. Here we describe a relatively rapid two-component transient expression assay that was used to identify a gene promoter active in the larval salivary glands of the green blow fly, Lucilia sericata. Sterile L.sericata maggots are widely used for wound debridement. A larval salivary gland gene promoter could be used to make maggots that secrete factors for enhanced wound therapy. Embryos from a line that carry a tetracycline transactivator (tTA)-activated red fluorescent protein gene were injected with plasmid DNA with the tTA gene driven by a constitutive or tissue-specific gene promoter. The hatched larvae were reared on diet and then examined for red fluorescence. A promoter from the LsCG30371 gene was active in the larval salivary glands. The tissue-specificity of the promoter was subsequently confirmed with stable transgenic lines that carried the LsCG30371-tTA gene. The relatively rapid transient expression assay could potentially be used to determine the tissue-specificity of other gene promoters. Further, the stable LsCG30371-tTA lines could be used to make sterile maggots that secrete factors from the salivary glands for enhanced wound healing.

Body plan evolvability: The role of variability in gene regulatory networks

Recent computational modeling of early fruit fly (Drosophila) development has characterized the degree to which gene regulation networks can be robust to natural variability. In the first few hours of development, broad spatial gradients of maternally derived transcription factors activate embryonic gap genes. These gap patterns determine the subsequent segmented insect body plan through pair-rule gene expression. Gap genes are expressed with greater spatial precision than the maternal patterns. Computational modeling of the gap-gap regulatory interactions provides a mechanistic understanding for this robustness to maternal variability in wild-type (WT) patterning. A long-standing question in evolutionary biology has been how a system which is robust, such as the developmental program creating any particular species' body plan, is also evolvable, i.e. how can a system evolve or speciate, if the WT form is strongly buffered and protected? In the present work, we use the WT model to explore the breakdown of such Waddington-type 'canalization'. What levels of variability will push the system out of the WT form; are there particular pathways in the gene regulatory mechanism which are more susceptible to losing the WT form; and when robustness is lost, what types of forms are most likely to occur (i.e. what forms lie near the WT)? Manipulating maternal effects in several different pathways, we find a common gap 'peak-to-step' pattern transition in the loss of WT. We discuss these results in terms of the evolvability of insect segmentation, and in terms of experimental perturbations and mutations which could test the model predictions. We conclude by discussing the prospects for using continuum models of pattern dynamics to investigate a wider range of evo-devo problems.

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.

Scale invariance in early embryonic development

The body plan of the fruit fly is determined by the expression of just a handful of genes. We show that the spatial patterns of expression for several of these genes scale precisely with the size of the embryo. Concretely, discrete positional markers such as the peaks in striped patterns have absolute positions along the anterior-posterior axis that are proportional to embryo length, with better than 1% accuracy. Further, the information (in bits) that graded patterns of expression provide about position can be decomposed into information about fractional or scaled position and information about absolute position or embryo length; all of the available information is about scaled position, again with ~ 1% accuracy. These observations suggest that the underlying genetic network exhibits scale invariance in a deeper mathematical sense. Taking this mathematical statement seriously requires that the network dynamics have a zero mode, which connects to many other observations on this system.

Pseudocleavage furrows restrict plasma membrane-associated PH domain in syncytial Drosophila embryos

Syncytial cells contain multiple nuclei and have local distribution and function of cellular components despite being synthesized in a common cytoplasm. The syncytial Drosophila blastoderm embryo shows reduced spread of organelle and plasma membrane-associated proteins between adjacent nucleo-cytoplasmic domains. Anchoring to the cytoarchitecture within a nucleo-cytoplasmic domain is likely to decrease the spread of molecules; however, its role in restricting this spread has not been assessed. In order to analyze the cellular mechanisms that regulate the rate of spread of plasma membrane-associated molecules in the syncytial Drosophila embryos, we express a pleckstrin homology (PH) domain in a localized manner at the anterior of the embryo by tagging it with the bicoid mRNA localization signal. Anteriorly expressed PH-domain forms an exponential gradient in the anteroposterior axis with a longer length scale as compared to Bicoid. Using a combination of experiments and theoretical modeling, we find that the characteristic distribution and length scale emerge due to plasma membrane sequestration and restriction within an energid. Loss of plasma membrane remodeling to form pseudocleavage furrows shows an enhanced spread of PH-domain but not Bicoid. Modeling analysis suggests that the enhanced spread of the PH-domain occurs due to the increased spread of the cytoplasmic population of the PH-domain in pseudocleavage furrow mutants. Our analysis of cytoarchitecture interaction in regulating plasma membrane protein distribution and constraining its spread has implications on the mechanisms of spread of various molecules such as morphogens in syncytial cells.

Modulating the bicoid gradient in space and time

Background

The formation of the Bicoid (Bcd) gradient in the early Drosophila is one of the most fascinating observations in biology and serves as a paradigm for gradient formation, yet its mechanism is still not fully understood. Two distinct models were proposed in the past, the SDD and the ARTS model.

Results

We define novel cis- and trans-acting factors that are indispensable for gradient formation. The first one is the poly A tail length of the bcd mRNA where we demonstrate that it changes not only in time, but also in space. We show that posterior bcd mRNAs possess a longer poly tail than anterior ones and this elongation is likely mediated by wispy (wisp), a poly A polymerase. Consequently, modulating the activity of Wisp results in changes of the Bcd gradient, in controlling downstream targets such as the gap and pair-rule genes, and also in influencing the cuticular pattern. Attempts to modulate the Bcd gradient by subjecting the egg to an extra nuclear cycle, i.e. a 15^th nuclear cycle by means of the maternal haploid (mh) mutation showed no effect, neither on the appearance of the gradient nor on the control of downstream target. This suggests that the segmental anlagen are determined during the first 14 nuclear cycles. Finally, we identify the Cyclin B (CycB) gene as a trans-acting factor that modulates the movement of Bcd such that Bcd movement is allowed to move through the interior of the egg.

Conclusions

Our analysis demonstrates that Bcd gradient formation is far more complex than previously thought requiring a revision of the models of how the gradient is formed.

Quantitative Analysis of the Dynamics of Maternal Gradients in the Early Drosophila Embryo

Predetermination, formation, and maintenance of the primary morphogenetic gradient (bicoid, bcd) of the early Drosophila embryo involves many interrelated processes. Here we focus on the biological systems analysis of the bcd mRNA redistribution in an early embryo. The results of the quantitative analysis of experimental data, together with the results of their dynamic modeling, substantiate the role of active transport in the redistribution of the bcd mRNA. The role of the nonlinearity of degradation mechanisms in the mRNA pattern robustness is discussed.

Growing Up in a Changing World: Environmental Regulation of Development in Insects

All organisms are exposed to changes in their environment throughout their life cycle. When confronted with these changes, they adjust their development and physiology to ensure that they can produce the functional structures necessary for survival and reproduction. While some traits are remarkably invariant, or robust, across environmental conditions, others show high degrees of variation, known as plasticity. Generally, developmental processes that establish cell identity are thought to be robust to environmental perturbation, while those relating to body and organ growth show greater degrees of plasticity. However, examples of plastic patterning and robust organ growth demonstrate that this is not a hard-and-fast rule.In this review, we explore how the developmental context and the gene regulatory mechanisms underlying trait formation determine the impacts of the environment on development in insects. Furthermore, we outline future issues that need to be resolved to understand how the structure of signaling networks defines whether a trait displays plasticity or robustness.

How to fit in: The learning principles of cell differentiation

Cell differentiation in multicellular organisms requires cells to respond to complex combinations of extracellular cues, such as morphogen concentrations. Some models of phenotypic plasticity conceptualise the response as a relatively simple function of a single environmental cues (e.g. a linear function of one cue), which facilitates rigorous analysis. Conversely, more mechanistic models such those implementing GRNs allows for a more general class of response functions but makes analysis more difficult. Therefore, a general theory describing how cells integrate multi-dimensional signals is lacking. In this work, we propose a theoretical framework for understanding the relationships between environmental cues (inputs) and phenotypic responses (outputs) underlying cell plasticity. We describe the relationship between environment and cell phenotype using logical functions, making the evolution of cell plasticity equivalent to a simple categorisation learning task. This abstraction allows us to apply principles derived from learning theory to understand the evolution of multi-dimensional plasticity. Our results show that natural selection is capable of discovering adaptive forms of cell plasticity associated with complex logical functions. However, developmental dynamics cause simpler functions to evolve more readily than complex ones. By using conceptual tools derived from learning theory we show that this developmental bias can be interpreted as a learning bias in the acquisition of plasticity functions. Because of that bias, the evolution of plasticity enables cells, under some circumstances, to display appropriate plastic responses to environmental conditions that they have not experienced in their evolutionary past. This is possible when the selective environment mirrors the bias of the developmental dynamics favouring the acquisition of simple plasticity functions–an example of the necessary conditions for generalisation in learning systems. These results illustrate the functional parallelisms between learning in neural networks and the action of natural selection on environmentally sensitive gene regulatory networks. This offers a theoretical framework for the evolution of plastic responses that integrate information from multiple cues, a phenomenon that underpins the evolution of multicellularity and developmental robustness.

In organisms composed of many cell types, the differentiation of cells relies on their ability to respond to complex extracellular cues, such as morphogen concentrations, a phenomenon known as cell plasticity. Although cell plasticity plays a crucial role in development and evolution, it is not clear how, and if, cell plasticity can enhance adaptation to a novel environment and/or facilitate robust developmental processes. In some models, the relationships between the environmental cues (inputs) and the phenotypic responses (outputs) are conceptualised as one-to-one (i.e. simple ‘reaction norms’); whereas the phenotype of plastic cells commonly depends on several simultaneous inputs (i.e. many-to-one, multi-dimensional reaction norms). One alternative is the use of a gene-regulatory network (GRN) models that allow for much more general responses; but this can make analysis difficult. In this work we use a theoretical framework based on logical functions and learning theory to characterize such multi-dimensional reaction norms produced by GRNs. This allows us to reveal a strong and previously unnoticed bias towards the acquisition of simple forms of cell plasticity, which increases their ability to adapt to novel environments. Recognising this bias helps us to understand when the evolution of cell plasticity will increase the ability of plastic cells to adapt to novel environments, to respond appropriately to complex extracellular cues and to enhance developmental robustness. Since this set of properties are required for the evolution of multicellularity, our approach can also contribute to our understanding of this evolutionary transition.

Embryonic geometry underlies phenotypic variation in decanalized conditions

During development, many mutations cause increased variation in phenotypic outcomes, a phenomenon termed decanalization. Phenotypic discordance is often observed in the absence of genetic and environmental variations, but the mechanisms underlying such inter-individual phenotypic discordance remain elusive. Here, using the anterior-posterior (AP) patterning of the Drosophila embryo, we identified embryonic geometry as a key factor predetermining patterning outcomes under decanalizing mutations. With the wild-type AP patterning network, we found that AP patterning is robust to variations in embryonic geometry; segmentation gene expression remains reproducible even when the embryo aspect ratio is artificially reduced by more than twofold. In contrast, embryonic geometry is highly predictive of individual patterning defects under decanalized conditions of either increased bicoid (bcd) dosage or bcd knockout. We showed that the phenotypic discordance can be traced back to variations in the gap gene expression, which is rendered sensitive to the geometry of the embryo under mutations.

Positional information and tissue scaling during development and regeneration

In order to contribute to the appropriate tissues during development, cells need to know their position within the embryo. This positional information is conveyed by gradients of signaling molecules, termed morphogens, that are produced in specific regions of the embryo and induce concentration-dependent responses in target tissues. Positional information is remarkably robust, and embryos often develop with the correct proportions even if large parts of the embryo are removed. In this Review, we discuss classical embryological experiments and modern quantitative analyses that have led to mechanistic insights into how morphogen gradients adapt, scale and properly pattern differently sized domains. We analyze these experimental findings in the context of mathematical models and synthesize general principles that apply to multiple systems across species and developmental stages.

Seeing is believing: the Bicoid protein reveals its path

In this commentary, I will review the latest findings on the Bicoid (Bcd) morphogen in Drosophila, a paradigm for gradient formation taught to biology students for more than two decades. “Seeing is believing” also summarizes the erroneous steps that were needed to elucidate the mechanisms of gradient formation and the path of movement of Bcd. Initially proclaimed as a dogma in 1988 and later incorporated into the SDD model where the broad diffusion of Bcd throughout the embryo was the predominant step leading to gradient formation, the SDD model was irrefutable for more than two decades until first doubts were raised in 2007 regarding the diffusion properties of Bcd associated with the SDD model. This led to re-thinking of the issue and the definition of a new model, termed the ARTS model which could explain most of the physical constraints that were inherently associated with the SDD model. In the ARTS model, gradient formation is mediated by the mRNA which is redistributed along cortical microtubules to form a mRNA gradient which is translated to form the protein gradient. Contrary to the SDD model, there is no Bcd diffusion from the tip. The ARTS model is also compatible with the observed cortical movement of Bcd. I will critically compare the SDD and the ARTS models as well as other models, analyze the major differences, and highlight the path where Bcd is localized during early nuclear cycles.

Scale-invariant patterning by size-dependent inhibition of Nodal signalling

Individuals can vary significantly in size, but the proportions of their body plans are often maintained. We generated smaller zebrafish by removing 30% of their cells at blastula stages and found that these embryos developed into normally patterned individuals. Strikingly, the proportions of all germ layers adjusted to the new embryo size within two hours after cell removal. Since Nodal/Lefty signalling controls germ layer patterning, we performed a computational screen for scale-invariant models of this activator/inhibitor system. This analysis predicted that the concentration of the highly diffusive inhibitor Lefty increases in smaller embryos, leading to a decreased Nodal activity range and contracted germ layer dimensions. In vivo studies confirmed that Lefty concentration increased in smaller embryos, and embryos with reduced Lefty levels or with diffusion-hindered Lefty failed to scale their tissue proportions. These results reveal that size-dependent inhibition of Nodal signalling allows scale-invariant patterning.

Size-reduced embryos reveal a gradient scaling-based mechanism for zebrafish somite formation

Little is known about how the sizes of animal tissues are controlled. A prominent example is somite size, which varies widely both within an individual and across species. Despite intense study of the segmentation clock governing the timing of somite generation, how it relates to somite size is poorly understood. Here, we examine somite scaling and find that somite size at specification scales with the length of the presomitic mesoderm (PSM) despite considerable variation in PSM length across developmental stages and in surgically size-reduced embryos. Measurement of clock period, axis elongation speed and clock gene expression patterns demonstrate that existing models fail to explain scaling. We posit a 'clock and scaled gradient' model, in which somite boundaries are set by a dynamically scaling signaling gradient across the PSM. Our model not only explains existing data, but also makes a unique prediction that we confirm experimentally - the formation of periodic 'echoes' in somite size following perturbation of the size of one somite. Our findings demonstrate that gradient scaling plays a central role in both progression and size control of somitogenesis.

LlamaTags: A Versatile Tool to Image Transcription Factor Dynamics in Live Embryos

Embryonic cell fates are defined by transcription factors that are rapidly deployed, yet attempts to visualize these factors in vivo often fail because of slow fluorescent protein maturation. Here, we pioneer a protein tag, LlamaTag, which circumvents this maturation limit by binding mature fluorescent proteins, making it possible to visualize transcription factor concentration dynamics in live embryos. Implementing this approach in the fruit fly Drosophila melanogaster, we discovered stochastic bursts in the concentration of transcription factors that are correlated with bursts in transcription. We further used LlamaTags to show that the concentration of protein in a given nucleus heavily depends on transcription of that gene in neighboring nuclei; we speculate that this inter-nuclear signaling is an important mechanism for coordinating gene expression to delineate straight and sharp boundaries of gene expression. Thus, LlamaTags now make it possible to visualize the flow of information along the central dogma in live embryos.

A stepwise model of reaction-diffusion and positional information governs self-organized human peri-gastrulation-like patterning

How position-dependent cell fate acquisition occurs during embryogenesis is a central question in developmental biology. To study this process, we developed a defined, high-throughput assay to induce peri-gastrulation-associated patterning in geometrically confined human pluripotent stem cell (hPSC) colonies. We observed that, upon BMP4 treatment, phosphorylated SMAD1 (pSMAD1) activity in the colonies organized into a radial gradient. We developed a reaction-diffusion (RD)-based computational model and observed that the self-organization of pSMAD1 signaling was consistent with the RD principle. Consequent fate acquisition occurred as a function of both pSMAD1 signaling strength and duration of induction, consistent with the positional-information (PI) paradigm. We propose that the self-organized peri-gastrulation-like fate patterning in BMP4-treated geometrically confined hPSC colonies arises via a stepwise model of RD followed by PI. This two-step model predicted experimental responses to perturbations of key parameters such as colony size and BMP4 dose. Furthermore, it also predicted experimental conditions that resulted in RD-like periodic patterning in large hPSC colonies, and rescued peri-gastrulation-like patterning in colony sizes previously thought to be reticent to this behavior.

Cortical movement of Bicoid in early Drosophila embryos is actin- and microtubule-dependent and disagrees with the SDD diffusion model

The Bicoid (Bcd) protein gradient in Drosophila serves as a paradigm for gradient formation in textbooks. The SDD model (synthesis, diffusion, degradation) was proposed to explain the formation of the gradient. The SDD model states that the bcd mRNA is located at the anterior pole of the embryo at all times and serves a source for translation of the Bicoid protein, coupled with diffusion and uniform degradation throughout the embryo. Recently, the ARTS model (active RNA transport, synthesis) challenged the SDD model. In this model, the mRNA is transported at the cortex along microtubules to form a mRNA gradient which serves as template for the production of Bcd, hence little Bcd movement is involved. To test the validity of the SDD model, we developed a sensitive assay to monitor the movement of Bcd during early nuclear cycles. We observed that Bcd moved along the cortex and not in a broad front towards the posterior as the SDD model would have predicted. We subjected embryos to hypoxia where the mRNA remained strictly located at the tip at all times, while the protein was allowed to move freely, thus conforming to an ideal experimental setup to test the SDD model. Unexpectedly, Bcd still moved along the cortex. Moreover, cortical Bcd movement was sparse, even under longer hypoxic conditions. Hypoxic embryos treated with drugs compromising microtubule and actin function affected Bcd cortical movement and stability. Vinblastine treatment allowed the simulation of an ideal SDD model whereby the protein moved throughout the embryo in a broad front. In unfertilized embryos, the Bcd protein followed the mRNA which itself was transported into the interior of the embryo utilizing a hitherto undiscovered microtubular network. Our data suggest that the Bcd gradient formation is probably more complex than previously anticipated.

Gene expression boundary scaling and organ size regulation in the Drosophila embryo

How the shape and size of tissues and organs is regulated during development is a major question in developmental biology. Such regulation relies upon both intrinsic cues (such as signaling networks) and extrinsic inputs (such as from neighboring tissues). Here, we focus on pattern formation and organ development during Drosophila embryogenesis. In particular, we outline the importance of both biochemical and mechanical tissue-tissue interactions in size regulation. We describe how the Drosophila embryo can potentially provide novel insights into how shape and size are regulated during development. We focus on gene expression boundary scaling in the early embryo and how size is regulated in three organs (hindgut, trachea, and ventral nerve cord) later in development, with particular focus on the role of tissue-tissue interactions. Overall, we demonstrate that Drosophila embryogenesis provides a suitable model system for studying spatial and temporal scaling and size control in vivo.

The Functionality and Evolution of Eukaryotic Transcriptional Enhancers

Enhancers regulate precise spatial and temporal patterns of gene expression in eukaryotes and, moreover, evolutionary changes in these modular cis-regulatory elements may represent the predominant genetic basis for phenotypic evolution. Here, we review approaches to identify and functionally analyze enhancers and their transcription factor binding sites, including assay for transposable-accessible chromatin-sequencing (ATAC-Seq) and clustered regularly interspaced short palindromic repeats (CRISPR)/Cas9, respectively. We also explore enhancer functionality, including how transcription factor binding sites combine to regulate transcription, as well as research on shadow and super enhancers, and how enhancers can act over great distances and even in trans. Finally, we discuss recent theoretical and empirical data on how transcription factor binding sites and enhancers evolve. This includes how the function of enhancers is maintained despite the turnover of transcription factor binding sites as well as reviewing studies where mutations in enhancers have been shown to underlie morphological change.

Emerging developmental genetic model systems in holometabolous insects

The number of insect species that are amenable to functional genetic studies is growing rapidly and provides many new research opportunities in developmental and evolutionary biology. The holometabolous insects represent a disproportionate percentage of animal diversity and are thus well positioned to provide model species for a wide variety of developmental processes. Here we discuss emerging holometabolous models, and review some recent breakthroughs. For example, flies and midges were found to use structurally unrelated long-range pattern organizers, butterflies and moths revealed extensive pattern formation during oogenesis, new imaging possibilities in the flour beetle Tribolium castaneum showed how embryos break free of their extraembryonic membranes, and the complex genetics governing interspecies difference in head shape were revealed in Nasonia wasps.

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.

Scaling of morphogenetic patterns in reaction-diffusion systems

Development of multicellular organisms is commonly associated with the response of individual cells to concentrations of chemical substances called morphogens. Concentration fields of morphogens form a basis for biological patterning and ensure its properties including ability to scale with the size of the organism. While mechanisms underlying the formation of morphogen gradients are reasonably well understood, little is known about processes responsible for their scaling. Here, we perform a formal analysis of scaling for chemical patterns forming in continuous systems. We introduce a quantity representing the sensitivity of systems to changes in their size and use it to analyse scaling properties of patterns forming in a few different systems. Particularly, we consider how scaling properties of morphogen gradients forming in diffusion-decay systems depend on boundary conditions and how the scaling can be improved by passive modulation of morphogens or active transport in the system. We also analyse scaling of morphogenetic signal caused by two opposing gradients and consider scaling properties of patterns forming in activator-inhibitor systems. We conclude with a few possible mechanisms which allow scaling of morphogenetic patterns.

Critical waves and the length problem of biology

It is pointed out that the mystery of how biological systems measure their lengths vanishes away if one premises that they have discovered a way to generate linear waves analogous to compressional sound. These can be used to detect length at either large or small scales using echo timing and fringe counting. It is shown that suitable linear chemical potential waves can, in fact, be manufactured by tuning to criticality conventional reaction-diffusion with a small number substance. Min oscillations in Escherichia coli are cited as precedent resonant length measurement using chemical potential waves analogous to laser detection. Mitotic structures in eukaryotes are identified as candidates for such an effect at higher frequency. The engineering principle is shown to be very general and functionally the same as that used by hearing organs.

A model for the expression of gap genes based on the Jeffreys-type equation

MOTIVATION

We propose the third-order model equation of the Jeffreys type for concentrations of gap gene proteins in order to take into account particle inertia. Gap genes are responsible for formation of body segments in Drosophila melanogaster embryo during its early development. Usually the expression of the genes is described by the model of protein transport based on conventional diffusion equation. However, the model is known to govern the Brownian (non-inertial) motion of particles; hence, it is hardly applicable to the description of protein transport.

RESULTS

Analysis of the Jeffreys-type equation results in the necessary condition for the problem to be well-posed. Application of the Jeffreys-type equation with non-linear terms to description of the dynamics of gap gene network demonstrates better fitting to experimental data than the conventional model.

AVAILABILITY AND IMPLEMENTATION

Implementation of solver algorithms and the software are freely available from: https://github.com/wswgG/solver-for-the-Jeffreys-type-equations-system .

Scaling morphogen gradients during tissue growth by a cell division rule

Morphogen gradients guide the patterning of tissues and organs during the development of multicellular organisms. In many cases, morphogen signaling is also required for tissue growth. The consequences of this interplay between growth and patterning are not well understood. In the Drosophila wing imaginal disc, the morphogen Dpp guides patterning and is also required for tissue growth. In particular, it was recently reported that cell division in the disc correlates with the temporal increase in Dpp signaling. Here we mathematically model morphogen gradient formation in a growing tissue, accounting also for morphogen advection and dilution. Our analysis defines a new scaling mechanism, which we term the morphogen-dependent division rule (MDDR): when cell division depends on the temporal increase in morphogen signaling, the morphogen gradient scales with the growing tissue size, tissue growth becomes spatially uniform and the tissue naturally attains a finite size. This model is consistent with many properties of the wing disc. However, we find that the MDDR is not consistent with the phenotype of scaling-defective mutants, supporting the view that temporal increase in Dpp signaling is not the driver of cell division during late phases of disc development. More generally, our results show that local coupling of cell division with morphogen signaling can lead to gradient scaling and uniform growth even in the absence of global feedbacks. The MDDR scaling mechanism might be particularly beneficial during rapid proliferation, when global feedbacks are hard to implement.

The embryo as a laboratory: quantifying transcription in Drosophila

Transcriptional regulation of gene expression is fundamental to most cellular processes, including determination of cellular fates. Quantitative studies of transcription in cultured cells have led to significant advances in identifying mechanisms underlying transcriptional control. Recent progress allowed implementation of these same quantitative methods in multicellular organisms to ask how transcriptional regulation unfolds both in vivo and at the single molecule level in the context of embryonic development. Here we review some of these advances in early Drosophila development, which bring the embryo on par with its single celled counterparts. In particular, we discuss progress in methods to measure mRNA and protein distributions in fixed and living embryos, and we highlight some initial applications that lead to fundamental new insights about molecular transcription processes. We end with an outlook on how to further exploit the unique advantages that come with investigating transcriptional control in the multicellular context of development.

Diversity of molecules and mechanisms in establishing insect anterior-posterior polarity

Anterior-posterior (AP) patterning is an essential process that requires the generation of large amounts of positional information to properly specify many distinct cell fates along the long axis of the insect embryo. While the general molecular basis of this process has long been known in the fly Drosophila, detailed understanding of this process is still emerging in other insect species. What is now clear is that this process in extremely labile, and distinct AP patterning programs can exist even within a single species. This review presents recent progress on this topic in an attempt to synthesize the disparate data and provide an outlook on the future of the field.

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.

Scaling of dorsal-ventral patterning in the Xenopus laevis embryo

Scaling of pattern with size has been described and studied for over a century, yet its molecular basis is understood in only a few cases. In a recent, elegant study, Inomata and colleagues proposed a new model explaining how bone morphogenic protein (BMP) activity gradient scales with embryo size in the early Xenopus laevis embryo. We discuss their results in conjunction with an alternative model we proposed previously. The expansion-repression mechanism (ExR) provides a conceptual framework unifying both mechanisms. Results of Inomata and colleagues implicate the chordin-stabilizing protein sizzled as the expander molecule enabling scaling, while we attributed this role to the BMP ligand Admp. The two expanders may work in concert, as suggested by the mathematical model of Inomata et al. We discuss approaches for differentiating the contribution of sizzled and Admp to pattern scaling.

Adaptation of the length scale and amplitude of the Bicoid gradient profile to achieve robust patterning in abnormally large Drosophila melanogaster embryos

The formation of patterns that are proportional to the size of the embryo is an intriguing but poorly understood feature of development. Molecular mechanisms controlling such proportionality, or scaling, can be probed through quantitative interrogations of the properties of morphogen gradients that instruct patterning. Recent studies of the Drosophila morphogen gradient Bicoid (Bcd), which is required for anterior-posterior (AP) patterning in the early embryo, have uncovered two distinct ways of scaling. Whereas between-species scaling is achieved by adjusting the exponential shape characteristic of the Bcd gradient profile, namely, its length scale or length constant (λ), within-species scaling is achieved through adjusting the profile's amplitude, namely, the Bcd concentration at the anterior (B0). Here, we report a case in which Drosophila melanogaster embryos exhibit Bcd gradient properties uncharacteristic of their size. The embryos under investigation were from a pair of inbred lines that had been artificially selected for egg size extremes. We show that B0 in the large embryos is uncharacteristically low but λ is abnormally extended. Although the large embryos have more total bcd mRNA than their smaller counterparts, as expected, its distribution is unusually broad. We show that the large and small embryos develop gene expression patterns exhibiting boundaries that are proportional to their respective lengths. Our results suggest that the large-egg inbred line has acquired compensating properties that counteract the extreme length of the embryos to maintain Bcd gradient properties necessary for robust patterning. Our study documents, for the first time to our knowledge, a case of within-species Bcd scaling achieved through adjusting the gradient profile's exponential shape characteristic, illustrating at a molecular level how a developmental system can follow distinct operational paths towards the goal of robust and scaled patterning.

Mathematical modelling in developmental biology

In recent decades, molecular and cellular biology has benefited from numerous fascinating developments in experimental technique, generating an overwhelming amount of data on various biological objects and processes. This, in turn, has led biologists to look for appropriate tools to facilitate systematic analysis of data. Thus, the need for mathematical techniques, which can be used to aid the classification and understanding of this ever-growing body of experimental data, is more profound now than ever before. Mathematical modelling is becoming increasingly integrated into biological studies in general and into developmental biology particularly. This review outlines some achievements of mathematics as applied to developmental biology and demonstrates the mathematical formulation of basic principles driving morphogenesis. We begin by describing a mathematical formalism used to analyse the formation and scaling of morphogen gradients. Then we address a problem of interplay between the dynamics of morphogen gradients and movement of cells, referring to mathematical models of gastrulation in the chick embryo. In the last section, we give an overview of various mathematical models used in the study of the developmental cycle of Dictyostelium discoideum, which is probably the best example of successful mathematical modelling in developmental biology.

Variation in the dorsal gradient distribution is a source for modified scaling of germ layers in Drosophila

Specification of germ layers along the dorsoventral axis by morphogenetic gradients is an ideal model to study scaling properties of gradients and cell fate changes during evolution. Classical anatomical studies in divergent insects (e.g., flies and grasshoppers) revealed that the neuroectodermal size is conserved and originates similar numbers of neuroblasts of homologous identity. In contrast, mesodermal domains vary significantly in closely related Drosophila species. To further investigate the underlying mechanisms of scaling of germ layers across Drosophila species, we quantified the Dorsal (Dl)/NF-κB gradient, the main morphogenetic gradient that initiates separation of the mesoderm, neuroectoderm, and ectoderm. We discovered a variable range of Toll activation across species and found that Dl activates mesodermal genes at the same threshold levels in melanogaster sibling species. We also show that the Dl gradient distribution can be modulated by nuclear size and packing densities. We propose that variation in mesodermal size occurs at a fast evolutionary rate and is an important mechanism to define the ventral boundary of the neuroectoderm.

Using the developmental gene bicoid to identify species of forensically important blowflies (Diptera: calliphoridae)

Identifying species of insects used to estimate postmortem interval (PMI) is a major subject in forensic entomology. Because forensic insect specimens are morphologically uniform and are obtained at various developmental stages, DNA markers are greatly needed. To develop new autosomal DNA markers to identify species, partial genomic sequences of the bicoid (bcd) genes, containing the homeobox and its flanking sequences, from 12 blowfly species (Aldrichina grahami, Calliphora vicina, Calliphora lata, Triceratopyga calliphoroides, Chrysomya megacephala, Chrysomya pinguis, Phormia regina, Lucilia ampullacea, Lucilia caesar, Lucilia illustris, Hemipyrellia ligurriens and Lucilia sericata; Calliphoridae: Diptera) were determined and analyzed. This study first sequenced the ten blowfly species other than C. vicina and L. sericata. Based on the bcd sequences of these 12 blowfly species, a phylogenetic tree was constructed that discriminates the subfamilies of Calliphoridae (Luciliinae, Chrysomyinae, and Calliphorinae) and most blowfly species. Even partial genomic sequences of about 500 bp can distinguish most blowfly species. The short intron 2 and coding sequences downstream of the bcd homeobox in exon 3 could be utilized to develop DNA markers for forensic applications. These gene sequences are important in the evolution of insect developmental biology and are potentially useful for identifying insect species in forensic science.

Comparative transcriptomics of early dipteran development

Background

Modern sequencing technologies have massively increased the amount of data available for comparative genomics. Whole-transcriptome shotgun sequencing (RNA-seq) provides a powerful basis for comparative studies. In particular, this approach holds great promise for emerging model species in fields such as evolutionary developmental biology (evo-devo).

Results

We have sequenced early embryonic transcriptomes of two non-drosophilid dipteran species: the moth midge Clogmia albipunctata, and the scuttle fly Megaselia abdita. Our analysis includes a third, published, transcriptome for the hoverfly Episyrphus balteatus. These emerging models for comparative developmental studies close an important phylogenetic gap between Drosophila melanogaster and other insect model systems. In this paper, we provide a comparative analysis of early embryonic transcriptomes across species, and use our data for a phylogenomic re-evaluation of dipteran phylogenetic relationships.

Conclusions

We show how comparative transcriptomics can be used to create useful resources for evo-devo, and to investigate phylogenetic relationships. Our results demonstrate that de novo assembly of short (Illumina) reads yields high-quality, high-coverage transcriptomic data sets. We use these data to investigate deep dipteran phylogenetic relationships. Our results, based on a concatenation of 160 orthologous genes, provide support for the traditional view of Clogmia being the sister group of Brachycera (Megaselia, Episyrphus, Drosophila), rather than that of Culicomorpha (which includes mosquitoes and blackflies).

Conservation and variation in Hox genes: how insect models pioneered the evo-devo field

Evolutionary developmental biology, or evo-devo, broadly investigates how body plan diversity and morphological novelties have arisen and persisted in nature. The discovery of Hox genes in Drosophila, and their subsequent identification in most other metazoans, led biologists to try to understand how embryonic genes crucial for proper development have changed to promote the vast morphological variation seen in nature. Insects are ideal model systems for studying this diversity and the mechanisms underlying it because phylogenetic relationships are well established, powerful genetic tools have been developed, and there are many examples of evolutionary specializations that have arisen in nature in different insect lineages, such as the jumping leg of orthopterans and the helmet structures of treehoppers. Here, we briefly introduce the field of evo-devo and Hox genes, discuss functional tools available to study early developmental genes in insects, and provide examples in which changes in Hox genes have contributed to changes in body plan or morphology.

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

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

Differential diffusivity of Nodal and Lefty underlies a reaction-diffusion patterning system

Biological systems involving short-range activators and long-range inhibitors can generate complex patterns. Reaction-diffusion models postulate that differences in signaling range are caused by differential diffusivity of inhibitor and activator. Other models suggest that differential clearance underlies different signaling ranges. To test these models, we measured the biophysical properties of the Nodal/Lefty activator/inhibitor system during zebrafish embryogenesis. Analysis of Nodal and Lefty gradients revealed that Nodals have a shorter range than Lefty proteins. Pulse-labeling analysis indicated that Nodals and Leftys have similar clearance kinetics, whereas fluorescence recovery assays revealed that Leftys have a higher effective diffusion coefficient than Nodals. These results indicate that differential diffusivity is the major determinant of the differences in Nodal/Lefty range and provide biophysical support for reaction-diffusion models of activator/inhibitor-mediated patterning.

Tempo and mode in evolution of transcriptional regulation

Perennial questions of evolutionary biology can be applied to gene regulatory systems using the abundance of experimental data addressing gene regulation in a comparative context. What is the tempo (frequency, rate) and mode (way, mechanism) of transcriptional regulatory evolution? Here we synthesize the results of 230 experiments performed on insects and nematodes in which regulatory DNA from one species was used to drive gene expression in another species. General principles of regulatory evolution emerge. Gene regulatory evolution is widespread and accumulates with genetic divergence in both insects and nematodes. Divergence in cis is more common than divergence in trans. Coevolution between cis and trans shows a particular increase over greater evolutionary timespans, especially in sex-specific gene regulation. Despite these generalities, the evolution of gene regulation is gene- and taxon-specific. The congruence of these conclusions with evidence from other types of experiments suggests that general principles are discoverable, and a unified view of the tempo and mode of regulatory evolution may be achievable.

Mathematics and biology: a Kantian view on the history of pattern formation theory

Driesch's statement, made around 1900, that the physics and chemistry of his day were unable to explain self-regulation during embryogenesis was correct and could be extended until the year 1972. The emergence of theories of self-organisation required progress in several areas including chemistry, physics, computing and cybernetics. Two parallel lines of development can be distinguished which both culminated in the early 1970s. Firstly, physicochemical theories of self-organisation arose from theoretical (Lotka 1910-1920) and experimental work (Bray 1920; Belousov 1951) on chemical oscillations. However, this research area gained broader acceptance only after thermodynamics was extended to systems far from equilibrium (1922-1967) and the mechanism of the prime example for a chemical oscillator, the Belousov-Zhabotinski reaction, was deciphered in the early 1970s. Secondly, biological theories of self-organisation were rooted in the intellectual environment of artificial intelligence and cybernetics. Turing wrote his The chemical basis of morphogenesis (1952) after working on the construction of one of the first electronic computers. Likewise, Gierer and Meinhardt's theory of local activation and lateral inhibition (1972) was influenced by ideas from cybernetics. The Gierer-Meinhardt theory provided an explanation for the first time of both spontaneous formation of spatial order and of self-regulation that proved to be extremely successful in elucidating a wide range of patterning processes. With the advent of developmental genetics in the 1980s, detailed molecular and functional data became available for complex developmental processes, allowing a new generation of data-driven theoretical approaches. Three examples of such approaches will be discussed. The successes and limitations of mathematical pattern formation theory throughout its history suggest a picture of the organism, which has structural similarity to views of the organic world held by the philosopher Immanuel Kant at the end of the eighteenth century.

Expansion-repression mechanism for scaling the Dpp activation gradient in Drosophila wing imaginal discs

Maintaining a proportionate body plan requires the adjustment or scaling of organ pattern with organ size. Scaling is a general property of developmental systems, yet little is known about its underlying molecular mechanisms. Using theoretical modeling, we examine how the Dpp activation gradient in the Drosophila wing imaginal disc scales with disc size. We predict that scaling is achieved through an expansion-repression mechanism [1] whose mediator is the widely diffusible protein Pentagone (Pent). Central to this mechanism is the repression of pent expression by Dpp signaling, which provides an effective size measurement, and the Pent-dependent expansion of the Dpp gradient, which adjusts the gradient with tissue size. We validate this mechanism experimentally by demonstrating that scaling requires Pent and further, that scaling is abolished when pent is ubiquitously expressed. The expansion-repression circuit can be readily implemented by a variety of molecular interactions, suggesting its general utilization for scaling morphogen gradients during development.

Morphogen gradients: from generation to interpretation

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

Scaling of the Bicoid morphogen gradient by a volume-dependent production rate

An important feature of development is the formation of patterns that are proportional to the overall size of the embryo. But how such proportionality, or scaling, is achieved mechanistically remains poorly understood. Furthermore, it is currently unclear whether organisms utilize similar or distinct mechanisms to achieve scaling within a species and between species. Here we investigate within-species scaling mechanisms for anterior-posterior (A-P) patterning in Drosophila melanogaster, focusing specifically on the properties of the Bicoid (Bcd) morphogen gradient. Using embryos from lines artificially selected for large and small egg volume, we show that large embryos have higher nuclear Bcd concentrations in the anterior than small embryos. This anterior difference leads to scaling properties of the Bcd gradient profiles: in broad regions of the large and small embryos along the A-P axis, normalizing their positions to embryo length reduces the differences in both the nuclear Bcd concentrations and Bcd-encoded positional information. We further trace the origin of Bcd gradient scaling by showing directly that large embryos have more maternally deposited bcd mRNA than small embryos. Our results suggest a simple model for how within-species Bcd gradient scaling can be achieved. In this model, the Bcd production rate, which is dependent on the total number of bcd mRNA molecules in the anterior, is scaled with embryo volume.

Does positive selection drive transcription factor binding site turnover? A test with Drosophila cis-regulatory modules

Transcription factor binding site(s) (TFBS) gain and loss (i.e., turnover) is a well-documented feature of cis-regulatory module (CRM) evolution, yet little attention has been paid to the evolutionary force(s) driving this turnover process. The predominant view, motivated by its widespread occurrence, emphasizes the importance of compensatory mutation and genetic drift. Positive selection, in contrast, although it has been invoked in specific instances of adaptive gene expression evolution, has not been considered as a general alternative to neutral compensatory evolution. In this study we evaluate the two hypotheses by analyzing patterns of single nucleotide polymorphism in the TFBS of well-characterized CRM in two closely related Drosophila species, Drosophila melanogaster and Drosophila simulans. An important feature of the analysis is classification of TFBS mutations according to the direction of their predicted effect on binding affinity, which allows gains and losses to be evaluated independently along the two phylogenetic lineages. The observed patterns of polymorphism and divergence are not compatible with neutral evolution for either class of mutations. Instead, multiple lines of evidence are consistent with contributions of positive selection to TFBS gain and loss as well as purifying selection in its maintenance. In discussion, we propose a model to reconcile the finding of selection driving TFBS turnover with constrained CRM function over long evolutionary time.

Conserved function of the Krüppel gap gene in the blowfly Lucilia sericata, despite anterior shift of expression

To determine whether expression patterns of segmentation genes found in Drosophila melanogaster can be scaled to pattern larger insects, we studied the expression of the Krüppel (Kr) gene in the blowfly Lucilia sericata. Compared with Drosophila Kr, L. sericata Kr showed an unexpected 10% shift of expression towards the anterior pole. Furthermore, expression domains not found in D. melanogaster were present at the blastoderm stage of L. sericata. To compare Kr activity and function, we employed RNA interference-mediated gene silencing. We found Kr phenotypes in L. sericata comparable with those observed in D. melanogaster, demonstrating that L. sericata Kr functions as a gap gene as it does in Drosophila. Our results show that, despite an anterior shift in expression, Kr function has remained conserved during the evolution of the blowflies.

The gap gene network

Gap genes are involved in segment determination during the early development of the fruit fly Drosophila melanogaster as well as in other insects. This review attempts to synthesize the current knowledge of the gap gene network through a comprehensive survey of the experimental literature. I focus on genetic and molecular evidence, which provides us with an almost-complete picture of the regulatory interactions responsible for trunk gap gene expression. I discuss the regulatory mechanisms involved, and highlight the remaining ambiguities and gaps in the evidence. This is followed by a brief discussion of molecular regulatory mechanisms for transcriptional regulation, as well as precision and size-regulation provided by the system. Finally, I discuss evidence on the evolution of gap gene expression from species other than Drosophila. My survey concludes that studies of the gap gene system continue to reveal interesting and important new insights into the role of gene regulatory networks in development and evolution.

Artificial selection on egg size perturbs early pattern formation in Drosophila melanogaster

Pattern formation in Drosophila embryogenesis has been widely investigated as a developmental and evolutionary model of robustness. To ask whether genetic variation for pattern formation is suppressed in this system, artificial selection for divergent egg size was used to challenge the scaling of even-skipped (eve) pattern formation in mitotic cycle 14 (stage 5) embryos of Drosophila melanogaster. Three-dimensional confocal imaging revealed shifts in the allometry of eve pair-rule stripes along both anterior–posterior (A–P) and dorsoventral (D–V) axes as a correlated response to egg size selection, indicating the availability of genetic variation for this buffered trait. Environmental perturbation was not required for the manifestation of this variation. The number of nuclei at the cellular blastoderm stage also changed in response to selection, with large-egg selected lines having more than 1000 additional nuclei relative to small-egg lines. This increase in nuclear number in larger eggs does not scale with egg size, however, as nuclear density is inversely correlated with egg length. Nuclear density varies along the A–P axis but does not correlate with the shift in eve stripe allometry between the selection treatments. Despite its macroevolutionary conservation, both eve stripe patterning and blastoderm cell number vary genetically both within and between closely related species.

Fates-shifted is an F-box protein that targets Bicoid for degradation and regulates developmental fate determination in Drosophila embryos

Bicoid (Bcd) is a morphogenetic protein that instructs patterning along the anterior-posterior (A-P) axis in Drosophila embryos. Despite extensive studies, what controls the formation of a normal concentration gradient of Bcd remains an unresolved and controversial question. In this report we show that Bcd protein degradation is mediated by the ubiquitin-proteasome pathway. We identify a novel F-box protein, encoded by fates-shifted (fsd), that plays an important role in Bcd protein degradation by targeting it for ubiquitination. Embryos from females lacking fsd have an altered Bcd gradient profile, resulting in a shift of the fatemap along the A-P axis. Our study represents a first experimental demonstration that, contrary to an alternative hypothesis, Bcd protein degradation is required for normal gradient formation and developmental fate determination.