Pre-steady-state decoding of the Bicoid morphogen gradient

Modelling the Bicoid gradient

Morphogen gradients provide embryonic tissues with positional information by inducing target genes at different concentration thresholds and thus at different positions. The Bicoid morphogen gradient in Drosophila melanogaster embryos has recently been analysed quantitatively, yet how it forms remains a matter of controversy. Several biophysical models that rely on production, diffusion and degradation have been formulated to account for the observed dynamics of the Bicoid gradient, but no one model can account for all its characteristics. Here, we discuss how existing data on this gradient fit the various proposed models and what aspects of gradient formation these models fail to explain. We suggest that knowing a few additional parameters, such as the lifetime of Bicoid, would help to identify and develop better models of Bicoid gradient formation.

Quantitative genetic interactions reveal biological modularity

Traditionally, research has been reductionist, characterizing the individual components of biological systems. But new technologies have increased the size and scope of biological data, and systems approaches have broadened the view of how these components are interconnected. Here, we discuss how quantitative mapping of genetic interactions enhances our view of biological systems, allowing their deeper interrogation across different biological scales.

Dynamic assignment and maintenance of positional identity in the ventral neural tube by the morphogen sonic hedgehog

Morphogens are secreted signalling molecules that act in a graded manner to control the pattern of cellular differentiation in developing tissues. An example is Sonic hedgehog (Shh), which acts in several developing vertebrate tissues, including the central nervous system, to provide positional information during embryonic patterning. Here we address how Shh signalling assigns the positional identities of distinct neuronal subtype progenitors throughout the ventral neural tube. Assays of intracellular signal transduction and gene expression indicate that the duration as well as level of signalling is critical for morphogen interpretation. Progenitors of the ventral neuronal subtypes are established sequentially, with progressively more ventral identities requiring correspondingly higher levels and longer periods of Shh signalling. Moreover, cells remain sensitive to changes in Shh signalling for an extended time, reverting to antecedent identities if signalling levels fall below a threshold. Thus, the duration of signalling is important not only for the assignment but also for the refinement and maintenance of positional identity. Together the data suggest a dynamic model for ventral neural tube patterning in which positional information corresponds to the time integral of Shh signalling. This suggests an alternative to conventional models of morphogen action that rely solely on the level of signalling.

Multiscale modeling of diffusion in the early Drosophila embryo

We developed a multiscale approach for the computationally efficient modeling of morphogen gradients in the syncytial Drosophila embryo, a single cell with multiple dividing nuclei. By using a homogenization technique, we derived a coarse-grained model with parameters that are explicitly related to the geometry of the syncytium and kinetics of nucleocytoplasmic shuttling. One of our main results is an accurate analytical approximation for the effective diffusivity of a morphogen molecule as a function of the nuclear density. We used this expression to explore the dynamics of the Bicoid morphogen gradient, a signal that patterns the anterior-posterior axis of the embryo. A similar approach can be used to analyze the dynamics of all three maternal morphogen gradients in Drosophila.

A two-dimensional simulation model of the bicoid gradient in Drosophila

Background

Bicoid (Bcd) is a Drosophila morphogenetic protein responsible for patterning the anterior structures in embryos. Recent experimental studies have revealed important insights into the behavior of this morphogen gradient, making it necessary to develop a model that can recapitulate the biological features of the system, including its dynamic and scaling properties.

Methodology/Principal Findings

We present a biologically realistic 2-D model of the dynamics of the Bcd gradient in Drosophila embryos. This model is based on equilibrium binding of Bcd molecules to non-specific, low affinity DNA sites throughout the Drosophila genome. It considers both the diffusion media within which the Bcd gradient is formed and the dynamic and other relevant properties of bcd mRNA from which Bcd protein is produced. Our model recapitulates key features of the Bcd protein gradient observed experimentally, including its scaling properties and the stability of its nuclear concentrations during development. Our simulation model also allows us to evaluate the effects of other biological activities on Bcd gradient formation, including the dynamic redistribution of bcd mRNA in early embryos. Our simulation results suggest that, in our model, Bcd protein diffusion is important for the formation of an exponential gradient in embryos.

Conclusions/Significance

The 2-D model described in this report is a simple and versatile simulation procedure, providing a quantitative evaluation of the Bcd gradient system. Our results suggest an important role of Bcd binding to non-specific, low-affinity DNA sites in proper formation of the Bcd gradient in our model. They demonstrate that highly complex biological systems can be effectively modeled with relatively few parameters.

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

Advances in image acquisition and informatics technology have led to organism-scale spatiotemporal atlases of gene expression and protein distributions. To maximize the utility of this information for the study of developmental processes, a new generation of mathematical models is needed for discovery and hypothesis testing. Here, we develop a data-driven, geometrically accurate model of early Drosophila embryonic bone morphogenetic protein (BMP)-mediated patterning. We tested nine different mechanisms for signal transduction with feedback, eight combinations of geometry and gene expression prepatterns, and two scale-invariance mechanisms for their ability to reproduce proper BMP signaling output in wild-type and mutant embryos. We found that a model based on positive feedback of a secreted BMP-binding protein, coupled with the experimentally measured embryo geometry, provides the best agreement with population mean image data. Our results demonstrate that using bioimages to build and optimize a three-dimensional model provides significant insights into mechanisms that guide tissue patterning.

Precision and scaling in morphogen gradient read-out

Morphogen gradients infer cell fate as a function of cellular position. Experiments in Drosophila embryos have shown that the Bicoid (Bcd) gradient is precise and exhibits some degree of scaling. We present experimental results on the precision of Bcd target genes for embryos with a single, double or quadruple dose of bicoid demonstrating that precision is highest at mid-embryo and position dependent, rather than gene dependent. This confirms that the major contribution to precision is achieved already at the Bcd gradient formation. Modeling this dynamic process, we investigate precision for inter-embryo fluctuations in different parameters affecting gradient formation. Within our modeling framework, the observed precision can only be achieved by a transient Bcd profile. Studying different extensions of our modeling framework reveals that scaling is generally position dependent and decreases toward the posterior pole. Our measurements confirm this trend, indicating almost perfect scaling except for anterior most expression domains, which overcompensate fluctuations in embryo length.

Quantitative imaging of the Dorsal nuclear gradient reveals limitations to threshold-dependent patterning in Drosophila

The NF-kappaB-related transcription factor, Dorsal, forms a nuclear concentration gradient in the early Drosophila embryo, patterning the dorsal-ventral (DV) axis to specify mesoderm, neurogenic ectoderm, and dorsal ectoderm cell fates. The concentration of nuclear Dorsal is thought to determine these patterning events; however, the levels of nuclear Dorsal have not been quantified previously. Furthermore, existing models of Dorsal-dependent germ layer specification and patterning consider steady-state levels of Dorsal relative to target gene expression patterns, yet both Dorsal gradient formation and gene expression are dynamic. We devised a quantitative imaging method to measure the Dorsal nuclear gradient while simultaneously examining Dorsal target gene expression along the DV axis. Unlike observations from other insects such as Tribolium, we find the Dorsal gradient maintains a constant bell-shaped distribution during embryogenesis. We also find that some classical Dorsal target genes are located outside the region of graded Dorsal nuclear localization, raising the question of whether these genes are direct Dorsal targets. Additionally, we show that Dorsal levels change in time during embryogenesis such that a steady state is not reached. These results suggest that the multiple gene expression outputs observed along the DV axis do not simply reflect a steady-state Dorsal nuclear gradient. Instead, we propose that the Dorsal gradient supplies positional information throughout nuclear cycles 10-14, providing additional evidence for the idea that compensatory combinatorial interactions between Dorsal and other factors effect differential gene expression along the DV axis.

Dynamics of the Dorsal morphogen gradient

The dorsoventral (DV) patterning of the Drosophila embryo depends on the nuclear localization gradient of Dorsal (Dl), a protein related to the mammalian NF-kappaB transcription factors. Current understanding of how the Dl gradient works has been derived from studies of its transcriptional interpretation, but the gradient itself has not been quantified. In particular, it is not known whether the Dl gradient is stable or dynamic during the DV patterning of the embryo. To address this question, we developed a mathematical model of the Dl gradient and constrained its parameters by experimental data. Based on our computational analysis, we predict that the Dl gradient is dynamic and, to a first approximation, can be described as a concentration profile with increasing amplitude and constant shape. These time-dependent properties of the Dl gradient are different from those of the Bicoid and MAPK phosphorylation gradients, which pattern the anterior and terminal regions of the embryo. Specifically, the gradient of the nuclear levels of Bicoid is stable, whereas the pattern of MAPK phosphorylation changes in both shape and amplitude. We attribute these striking differences in the dynamics of maternal morphogen gradients to the differences in the initial conditions and chemistries of the anterior, DV, and terminal systems.

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

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

Modelling the Drosophila embryo

I provide a historical overview on the use of mathematical models to gain insight into pattern formation during early development of the fruit fly Drosophila melanogaster. It is my intention to illustrate how the aims and methodology of modelling have changed from the early beginnings of a theoretical developmental biology in the 1960s to modern-day systems biology. I show that even early modelling attempts addressed interesting and relevant questions, which were not tractable by experimental approaches. Unfortunately, their validation was severely hampered by a lack of specificity and appropriate experimental evidence. There is a simple lesson to be learned from this: we cannot deduce general rules for pattern formation from first principles or spurious reproduction of developmental phenomena. Instead, we must infer such rules (if any) from detailed and accurate studies of specific developmental systems. To achieve this, mathematical modelling must be closely integrated with experimental approaches. I report on progress that has been made in this direction in the past few years and illustrate the kind of novel insights that can be gained from such combined approaches. These insights demonstrate the great potential (and some pitfalls) of an integrative, systems-level investigation of pattern formation.

Morphogen profiles can be optimized to buffer against noise

Morphogen profiles play a vital role in biology by specifying position in embryonic development. However, the factors that influence the shape of a morphogen profile remain poorly understood. Since morphogens should provide precise positional information, one significant factor is the robustness of the profile to noise. We compare three experimentally relevant classes of morphogen profiles (linear, exponential, and algebraic) to see which is most precise when subject to both external embryo-to-embryo fluctuations and internal fluctuations due to intrinsically random processes such as diffusion. We find that both the kinetic parameters and the overall gradient shape (e.g., exponential versus algebraic) can be optimized to generate maximally precise positional information.

Dynamic interpretation of hedgehog signaling in the Drosophila wing disc

Morphogens are classically defined as molecules that control patterning by acting at a distance to regulate gene expression in a concentration-dependent manner. In the Drosophila wing imaginal disc, secreted Hedgehog (Hh) forms an extracellular gradient that organizes patterning along the anterior-posterior axis and specifies at least three different domains of gene expression. Although the prevailing view is that Hh functions in the Drosophila wing disc as a classical morphogen, a direct correspondence between the borders of these patterns and Hh concentration thresholds has not been demonstrated. Here, we provide evidence that the interpretation of Hh signaling depends on the history of exposure to Hh and propose that a single concentration threshold is sufficient to support multiple outputs. Using mathematical modeling, we predict that at steady state, only two domains can be defined in response to Hh, suggesting that the boundaries of two or more gene expression patterns cannot be specified by a static Hh gradient. Computer simulations suggest that a spatial "overshoot" of the Hh gradient occurs, i.e., a transient state in which the Hh profile is expanded compared to the Hh steady-state gradient. Through a temporal examination of Hh target gene expression, we observe that the patterns initially expand anteriorly and then refine, providing in vivo evidence for the overshoot. The Hh gene network architecture suggests this overshoot results from the Hh-dependent up-regulation of the receptor, Patched (Ptc). In fact, when the network structure was altered such that the ptc gene is no longer up-regulated in response to Hh-signaling activation, we found that the patterns of gene expression, which have distinct borders in wild-type discs, now overlap. Our results support a model in which Hh gradient dynamics, resulting from Ptc up-regulation, play an instructional role in the establishment of patterns of gene expression.

Synchronous and stochastic patterns of gene activation in the Drosophila embryo

Drosophila embryogenesis is characterized by rapid transitions in gene activity, whereby crudely distributed gradients of regulatory proteins give way to precise on/off patterns of gene expression. To explore the underlying mechanisms, a partially automated, quantitative in situ hybridization method was used to visualize expression profiles of 14 developmental control genes in hundreds of embryos. These studies revealed two distinct patterns of gene activation: synchronous and stochastic. Synchronous genes display essentially uniform expression of nascent transcripts in all cells of an embryonic tissue, whereas stochastic genes display erratic patterns of de novo activation. RNA polymerase II is "pre-loaded" (stalled) in the promoter regions of synchronous genes, but not stochastic genes. Transcriptional synchrony might ensure the orderly deployment of the complex gene regulatory networks that control embryogenesis.

Morphogen gradient formation

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

Stable, precise, and reproducible patterning of bicoid and hunchback molecules in the early Drosophila embryo

Precise patterning of morphogen molecules and their accurate reading out are of key importance in embryonic development. Recent experiments have visualized distributions of proteins in developing embryos and shown that the gradient of concentration of Bicoid morphogen in Drosophila embryos is established rapidly after fertilization and remains stable through syncytial mitoses. This stable Bicoid gradient is read out in a precise way to distribute Hunchback with small fluctuations in each embryo and in a reproducible way, with small embryo-to-embryo fluctuation. The mechanisms of such stable, precise, and reproducible patterning through noisy cellular processes, however, still remain mysterious. To address these issues, here we develop the one- and three-dimensional stochastic models of the early Drosophila embryo. The simulated results show that the fluctuation in expression of the hunchback gene is dominated by the random arrival of Bicoid at the hunchback enhancer. Slow diffusion of Hunchback protein, however, averages out this intense fluctuation, leading to the precise patterning of distribution of Hunchback without loss of sharpness of the boundary of its distribution. The coordinated rates of diffusion and transport of input Bicoid and output Hunchback play decisive roles in suppressing fluctuations arising from the dynamical structure change in embryos and those arising from the random diffusion of molecules, and give rise to the stable, precise, and reproducible patterning of Bicoid and Hunchback distributions.

Establishing and interpreting graded Sonic Hedgehog signaling during vertebrate neural tube patterning: the role of negative feedback

The secreted protein Sonic Hedgehog (SHH) acts in graded fashion to pattern the dorsal-ventral axis of the vertebrate neural tube. This is a dynamic process in which increasing concentrations and durations of exposure to SHH generate neurons with successively more ventral identities. Interactions between the receiving cells and the graded signal underpin the mechanism of SHH action. In particular, negative feedback, involving proteins transcriptionally induced or repressed by SHH signaling, plays an essential role in shaping the graded readout. On one hand, negative feedback controls, in a noncell-autonomous manner, the distribution of SHH across the field of receiving cells. On the other, it acts cell-autonomously to convert different concentrations of SHH into distinct durations of intracellular signal transduction. Together, these mechanisms exemplify a strategy for morphogen interpretation, which we have termed temporal adaptation that relies on the continuous processing and refinement of the cellular response to the graded signal.

Accuracy of positional information provided by multiple morphogen gradients with correlated noise

Normal development of multicellular organisms requires cells to respond properly according to their positions. Positional information is often provided to cells as concentrations of diffusive chemicals called morphogens with spatial gradients. However, the spatial profiles of their concentrations include various kinds of noises, making positional information unreliable. In many developmental systems, multiple morphogen gradients are adopted to specify the spatial position along a single axis, presumably to achieve a sufficiently high precision of information on the location of each cell. In this paper, we ask how the precision of positional information depends on the number of morphogens. We derive a formula for the limit of precision when each cell adopts the maximum-likelihood estimation of the "true" position from noisy inputs. The precision increases with the number of morphogens and interestingly it also depends on the correlation of noises. The positional specification can be made more precisely if their gradients are of the opposite (same) direction when noises of the two morphogens are positively (negatively) correlated. The formula also tells us a minimum number of morphogens needed to achieve a given precision of positional information. We illustrate the theory by analyzing experimental data for the gradients of two diffusive chemicals, Bicoid and Caudal, in the early development of Drosophila embryo. The analysis suggests that combined information provided by the two chemicals is able to give accurate positional information in the middle part of the embryo, where the embryo segmentation occurs in later stages, much more than near both ends.

Formation of the bicoid morphogen gradient: an mRNA gradient dictates the protein gradient

The Bicoid (Bcd) protein gradient is generally believed to be established in pre-blastoderm Drosophila embryos by the diffusion of Bcd protein after translation of maternal mRNA, which serves as a strictly localized source of Bcd at the anterior pole. However, we previously published evidence that the Bcd gradient is preceded by a bcd mRNA gradient. Here, we have revisited and extended this observation by showing that the bcd mRNA and Bcd protein gradient profiles are virtually identical at all times. This confirms our previous conclusion that the Bcd gradient is produced by a bcd mRNA gradient rather than by diffusion. Based on our observation that bcd mRNA colocalizes with Staufen (Stau), we propose that the bcd mRNA gradient forms by a novel mechanism involving quasi-random active transport of a Stau-bcd mRNA complex through a nonpolar microtubular network, which confines the bcd mRNA to the cortex of the embryo.

Analysis of dynamic morphogen scale invariance

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

Canalization of gene expression in the Drosophila blastoderm by gap gene cross regulation

Developing embryos exhibit a robust capability to reduce phenotypic variations that occur naturally or as a result of experimental manipulation. This reduction in variation occurs by an epigenetic mechanism called canalization, a phenomenon which has resisted understanding because of a lack of necessary molecular data and of appropriate gene regulation models. In recent years, quantitative gene expression data have become available for the segment determination process in the Drosophila blastoderm, revealing a specific instance of canalization. These data show that the variation of the zygotic segmentation gene expression patterns is markedly reduced compared to earlier levels by the time gastrulation begins, and this variation is significantly lower than the variation of the maternal protein gradient Bicoid. We used a predictive dynamical model of gene regulation to study the effect of Bicoid variation on the downstream gap genes. The model correctly predicts the reduced variation of the gap gene expression patterns and allows the characterization of the canalizing mechanism. We show that the canalization is the result of specific regulatory interactions among the zygotic gap genes. We demonstrate the validity of this explanation by showing that variation is increased in embryos mutant for two gap genes, Krüppel and knirps, disproving competing proposals that canalization is due to an undiscovered morphogen, or that it does not take place at all. In an accompanying article in PLoS Computational Biology (doi:10.1371/journal.pcbi.1000303), we show that cross regulation between the gap genes causes their expression to approach dynamical attractors, reducing initial variation and providing a robust output. These results demonstrate that the Bicoid gradient is not sufficient to produce gap gene borders having the low variance observed, and instead this low variance is generated by gap gene cross regulation. More generally, we show that the complex multigenic phenomenon of canalization can be understood at a quantitative and predictive level by the application of a precise dynamical model.

Animals have an astonishing ability to develop reliably in spite of variable conditions during embryogenesis. More than 60 years ago, it was proposed that this property of development, called canalization, results from genetic interactions that adjust biochemical reactions so as to bring about reliable outcomes. Since then, a great deal of progress has been made in understanding the buffering of genotypic and environmental variation, and individual mutations that reveal variation have been identified. However, the mechanisms by which genetic interactions produce canalization are not yet well understood, because this requires molecular data on multiple developmental determinants and models that correctly predict complex interactions. We make use of gene expression data at both high spatial and temporal resolution for the gap genes involved in the segmentation of Drosophila. We also apply a mathematical model to show that cross regulation among the gap genes is responsible for canalization in this system. Furthermore, the model predicted specific interactions that cause canalization, and the prediction was validated experimentally. Our results show that groups of genes can act on one another to reduce variation and highlights the importance of genetic networks in generating robust development.

DuringDrosophila development, the expression patterns of gap genes are much less variable than the Bicoid morphogen gradient. Modeling and experiments show that this specific instance of canalization or developmental robustness occurs by gap gene cross regulation.

Anterior-posterior positional information in the absence of a strong Bicoid gradient

The Bicoid (Bcd) transcription factor is distributed as a long-range concentration gradient along the anterior posterior (AP) axis of the Drosophila embryo. Bcd is required for the activation of a series of target genes, which are expressed at specific positions within the gradient. Here we directly tested whether different concentration thresholds within the Bcd gradient establish the relative positions of its target genes by flattening the gradient and systematically varying expression levels. Genome-wide expression profiles were used to estimate the total number of Bcd target genes, and a general correlation was found between the Bcd concentration required for activation and the positions where target genes are expressed in wild-type embryos. However, concentrations required for target gene activation in embryos with flattened Bcd were consistently lower than those present at each target gene's position in the wild-type gradient, suggesting that Bcd is in excess at every position along the AP axis. Also, several Bcd target genes were positioned in correctly ordered stripes in embryos with flattened Bcd, and we suggest that these stripes are normally regulated by interactions between Bcd and the terminal patterning system. Our findings argue strongly against the strict interpretation of the Bcd morphogen hypothesis, and support the idea that target gene positioning involves combinatorial interactions that are mediated by the binding site architecture of each gene's cis-regulatory elements.

Determining the scale of the Bicoid morphogen gradient

Bicoid is a morphogen that sets up the anterior-posterior axis in early Drosophila embryos. Although the form of the Bicoid profile is consistent with a simple diffusion/degradation model, the observed length scale is much larger than should be expected based on the measured diffusion rate. Here, we study two possible mechanisms that could, in principle, affect this gradient and, hence, address this disagreement. First, we show that including trapping and release of Bicoid by the nuclei during cleavage cycles does not alter the morphogen length scale. More crucially, the inclusion of advective transport due to cytoplasmic streaming can have a large effect. Specifically, we build a simple model based on the (limited) experimental data and show that such a flow can lead to a Bicoid profile that is consistent with various experimental features. Specifically, the observed length scale is obtained, a steady profile is established, and improved scaling between embryos of different lengths is demonstrated.

Probing intrinsic properties of a robust morphogen gradient in Drosophila

A remarkable feature of development is its reproducibility, the ability to correct embryo-to-embryo variations and instruct precise patterning. In Drosophila, embryonic patterning along the anterior-posterior axis is controlled by the morphogen gradient Bicoid (Bcd). In this article, we describe quantitative studies of the native Bcd gradient and its target Hunchback (Hb). We show that the native Bcd gradient is highly reproducible and is itself scaled with embryo length. While a precise Bcd gradient is necessary for precise Hb expression, it still has positional errors greater than Hb expression. We describe analyses further probing mechanisms for Bcd gradient scaling and correction of its residual positional errors. Our results suggest a simple model of a robust Bcd gradient sufficient to achieve scaled and precise activation of its targets. The robustness of this gradient is conferred by its intrinsic properties of "self-correcting" the inevitable input variations to achieve a precise and reproducible output.

A precise Bicoid gradient is nonessential during cycles 11-13 for precise patterning in the Drosophila blastoderm

Background

During development, embryos decode maternal morphogen inputs into highly precise zygotic gene expression. The discovery of the morphogen Bicoid and its profound effect on developmental programming in the Drosophila embryo has been a cornerstone in understanding the decoding of maternal inputs. Bicoid has been described as a classical morphogen that forms a concentration gradient along the antero-posterior axis of the embryo by diffusion and initiates expression of target genes in a concentration-dependent manner in the syncytial blastoderm. Recent work has emphasized the stability of the Bicoid gradient as a function of egg length and the role of nuclear dynamics in maintaining the Bicoid gradient. Bicoid and nuclear dynamics were observed but not modulated under the ideal conditions used previously. Therefore, it has not been tested explicitly whether a temporally stable Bicoid gradient prior to cellularization is required for precise patterning.

Principal Findings

Here, we modulate both nuclear dynamics and the Bicoid gradient using laminar flows of different temperature in a microfluidic device to determine if stability of the Bicoid gradient prior to cellularization is essential for precise patterning. Dramatic motion of both cytoplasm and nuclei was observed prior to cellularization, and the Bicoid gradient was disrupted by nuclear motion and was highly abnormal as a function of egg length. Despite an abnormal Bicoid gradient during cycles 11–13, Even-skipped patterning in these embryos remained precise.

Conclusions

These results indicate that the stability of the Bicoid gradient as a function of egg length is nonessential during syncytial blastoderm stages. Further, presumably no gradient formed by simple diffusion on the scale of egg length could be responsible for the robust antero-posterior patterning observed, as severe cytoplasmic and nuclear motion would disrupt such a gradient. Additional mechanisms for how the embryo could sense its dimensions and interpret the Bicoid gradient are discussed.

Dynamics of maternal morphogen gradients in Drosophila

The first direct studies of morphogen gradients were done in the end of 1980s, in the early Drosophila embryo, which is patterned under the action of four maternally determined morphogens. Since the early studies of maternal morphogens were done with fixed embryos, they were viewed as relatively static signals. Several recent studies analyze dynamics of the anterior, dorsoventral, and terminal patterning signals. The results of these quantitative studies provide critical tests of classical models and reveal new modes of morphogen regulation and readout in one of the most extensively studied patterning systems.

Precision of the Dpp gradient

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

Optimal placement of multiple morphogen sources

During development, cells grow, differentiate, divide, and die according to their spatial positions, yet the positional information given to cells by morphogens (diffusive chemicals) includes considerable noises from various origins. In this paper, we examine a relationship between fluctuations in morphogen concentrations that the cells receive and the precision of positional specification by the morphogens in multidimensional space. As a method to quantify the precision, we introduce a measure of "ambiguity of positional information," based on the information entropy. We discover that the location of morphogen sources crucially affects the ambiguity, and that the ambiguity becomes minimum when the angle made by gradient vectors of different morphogens cross at a right angle in a target region under a given organ geometry (orthogonality principle). We conjecture that morphogen sources in development might be placed at the nearly optimal position that minimizes the ambiguity of positional information. This is supported by experimental data on the configurations of two major sources of spatial patterning, the apical ectodermal ridge (AER) and the zone of polarizing activity (ZPA), in vertebrate limb development. Indeed, their predicted configuration agrees very well with the one observed in experiments. We believe that the placement of morphogen sources to minimize the ambiguity of positional information is a basic principle in development of multicellular organisms beyond this particular example.

Theoretical and experimental approaches to understand morphogen gradients

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

The Decapentaplegic morphogen gradient: a precise definition

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

Pipeline for acquisition of quantitative data on segmentation gene expression from confocal images

We describe a data pipeline developed to extract the quantitative data on segmentation gene expression from confocal images of gene expression patterns in Drosophila. The pipeline consists of five steps: image segmentation, background removal, temporal characterization of an embryo, data registration and data averaging. This pipeline was successfully applied to obtain quantitative gene expression data at cellular resolution in space and at the 6.5-minute resolution in time, as well as to construct a spatiotemporal atlas of segmentation gene expression. Each data pipeline step can be easily adapted to process a wide range of images of gene expression patterns.

Border formation in a Bmp gradient reduced to single dissociated cells

Conversions of signaling gradients into sharp "all-or-none" borders are fundamental to tissue and organismal development. However, whether such conversions can be meaningfully reduced to dissociated cells in culture has been uncertain. Here we describe ultrasensitivity, the phenomenon equivalent to an all-or-none response, in dissociated neural precursor cells (NPCs) exposed to bone morphogenetic protein 4 (Bmp4). NPC ultrasensitivity is evident at the population and single-cell levels based on Msx1 induction, a well known Bmp target response, and occurs in the context of gene expression changes consistent with Bmp4 activity as a morphogen. Dissociated NPCs also display immediate early kinetics and irreversibility for Msx1 induction after brief Bmp4 exposure, which are attractive features for initial border formation. Relevance to border formation in vivo is provided by Bmp4 gain-of-function studies in explants and evidence for single-cell ultrasensitivity in normal and mutant Bmp gradient contexts in the developing forebrain. Together, these studies demonstrate relatively simple, robust, and reducible cell-intrinsic properties that contribute to developmental border formation within a signaling gradient.

Complex regulation of cyp26a1 creates a robust retinoic acid gradient in the zebrafish embryo

Positional identities along the anterior–posterior axis of the vertebrate nervous system are assigned during gastrulation by multiple posteriorizing signals, including retinoic acid (RA), fibroblast growth factors (Fgfs), and Wnts. Experimental evidence has suggested that RA, which is produced in paraxial mesoderm posterior to the hindbrain by aldehyde dehydrogenase 1a2 (aldh1a2/raldh2), forms a posterior-to-anterior gradient across the hindbrain field, and provides the positional information that specifies the locations and fates of rhombomeres. Recently, alternative models have been proposed in which RA plays only a permissive role, signaling wherever it is not degraded. Here we use a combination of experimental and modeling tools to address the role of RA in providing long-range positional cues in the zebrafish hindbrain. Using cell transplantation and implantation of RA-coated beads into RA-deficient zebrafish embryos, we demonstrate that RA can directly convey graded positional information over long distances. We also show that expression of Cyp26a1, the major RA-degrading enzyme during gastrulation, is under complex feedback and feedforward control by RA and Fgf signaling. The predicted consequence of such control is that RA gradients will be both robust to fluctuations in RA synthesis and adaptive to changes in embryo length during gastrulation. Such control also provides an explanation for the fact that loss of an endogenous RA gradient can be compensated for by RA that is provided in a spatially uniform manner.

The formation of gradients of morphogens, signaling molecules that determine cell fates in a concentration-dependent manner, is a fundamental process in developmental biology. Several morphogens pattern the anterior–posterior (head to tail) axis of the vertebrate nervous system, including the vitamin A derivative, retinoic acid (RA) and fibroblast growth factors (Fgfs). However, it remains unclear how the activities of such morphogen gradients are coordinated. We have addressed this question by combining genetic experiments in zebrafish and computational analyses. We show that RA acts as a graded signal over long distances and that its gradient is shaped, to a large extent, by local control of RA degradation. In particular, RA promotes and Fgf suppresses RA degradation, thereby linking the shapes of RA and Fgf gradients. Computational models suggest that this linkage helps make RA-mediated patterning robust to changes in the rate at which RA is synthesized (which may vary with levels of dietary vitamin A) as well as in the size and shape of the embryo during development. Analogous regulatory loops may be used for similar purposes in other tissues in which RA and Fgfs interact, as well as in other morphogen systems.

Experimental and computational studies in zebrafish reveal a complex system regulating degradation of the vitamin A derivative retinoic acid along the anterior-posterior axis, which helps explain how morphogen gradients are established and maintained.

Can we build synthetic, multicellular systems by controlling developmental signaling in space and time?

Using biological machinery to make new, functional molecules is an exciting area in chemical biology. Complex molecules containing both 'natural' and 'unnatural' components are made by processes ranging from enzymatic catalysis to the combination of molecular biology with chemical tools. Here, we discuss applying this approach to the next level of biological complexity -- building synthetic, functional biotic systems by manipulating biological machinery responsible for development of multicellular organisms. We describe recent advances enabling this approach, including first, recent developmental biology progress unraveling the pathways and molecules involved in development and pattern formation; second, emergence of microfluidic tools for delivering stimuli to a developing organism with exceptional control in space and time; third, the development of molecular and synthetic biology toolsets for redesigning or de novo engineering of signaling networks; and fourth, biological systems that are especially amendable to this approach.

Modeling the bicoid gradient: diffusion and reversible nuclear trapping of a stable protein

The Bicoid gradient in the Drosophila embryo provided the first example of a morphogen gradient studied at the molecular level. The exponential shape of the Bicoid gradient had always been interpreted within the framework of the localized production, diffusion, and degradation model. We propose an alternative mechanism, which assumes no Bicoid degradation. The medium where the Bicoid gradient is formed and interpreted is very dynamic. Most notably, the number of nuclei changes over three orders of magnitude from fertilization, when Bicoid synthesis is initiated, to nuclear cycle 14 when most of the measurements were taken. We demonstrate that a model based on Bicoid diffusion and nucleocytoplasmic shuttling in the presence of the growing number of nuclei can account for most of the properties of the Bicoid concentration profile. Consistent with experimental observations, the Bicoid gradient in our model is established before nuclei migrate to the periphery of the embryo and remains stable during subsequent nuclear divisions.

Canalization of segmentation and its evolution in Drosophila

Segmentation in Drosophila embryogenesis occurs through a hierarchical cascade of regulatory gene expression driven by the establishment of a diffusion-mediated morphogen gradient. Here, we investigate the response of this pattern formation process to genetic variation and evolution in egg size. Specifically, we ask whether spatial localization of gap genes Kruppel (Kr) and giant (gt) and the pair-rule gene even-skipped (eve) during cellularization is robust to genetic variation in embryo length in three Drosophila melanogaster isolines and two closely related species. We identified two wild-derived strains of D. melanogaster whose eggs differ by approximately 25% in length when reared under identical conditions. These two lines, a D. melanogaster laboratory stock (w1118), and offspring from crosses between the lines all exhibit precise scaling in the placement of gap and pair-rule gene expression along the anterior-posterior axis in relation to embryo length. Genetic analysis indicates that this scaling is maternally controlled. Maternal regulation of scaling must be required for consistent localization of segmentation gene expression because embryo size, a genetically variable and adaptive trait, is maternally inherited. We also investigated spatial scaling between these D. melanogaster lines and single lines of Drosophila sechellia and Drosophila simulans, the latter two differing by approximately 25% in egg length. In contrast to the robust scaling we observed within species, localization of gene expression relative to embryo length differs significantly between the three species. Thus, the developmental mechanism that assures robust scaling within a species does not prevent rapid evolution between species.

A mechanism for the sharp transition of morphogen gradient interpretation in Xenopus

Background

One way in which positional information is established during embryonic development is through the graded distribution of diffusible morphogens. Unfortunately, little is known about how cells interpret different concentrations of morphogen to activate different genes or how thresholds are generated in a morphogen gradient.

Results

Here we show that the concentration-dependent induction of the T-box transcription factor Brachyury (Xbra) and the homeobox-containing gene Goosecoid (Gsc) by activin in Xenopus can be explained by the dynamics of a simple network consisting of three elements with a mutual negative feedback motif that can function to convert a graded signal (activin) into a binary output (Xbra on and Gsc off, or vice versa). Importantly, such a system can display sharp thresholds. Consistent with the predictions of our model, Xenopus ectodermal cells display a binary response at the single cell level after treatment with activin.

Conclusion

This kind of simple network with mutual negative feedback might provide a general mechanism for selective gene activation in response to different levels of a single external signal. It provides a mechanism by which a sharp boundary might be created between domains of different cell types in response to a morphogen gradient.

Systems biology of embryonic morphogens

A network of secreted proteins that interact with each other in the extracellular space regulates embryonic morphogenesis. Mathematical modeling offers an excellent opportunity to understand how morphogens signal and self-regenerate pattern.

Enhancer responses to similarly distributed antagonistic gradients in development

Formation of spatial gene expression patterns in development depends on transcriptional responses mediated by gene control regions, enhancers. Here, we explore possible responses of enhancers to overlapping gradients of antagonistic transcriptional regulators in the Drosophila embryo. Using quantitative models based on enhancer structure, we demonstrate how a pair of antagonistic transcription factor gradients with similar or even identical spatial distributions can lead to the formation of distinct gene expression domains along the embryo axes. The described mechanisms are sufficient to explain the formation of the anterior and the posterior knirps expression, the posterior hunchback expression domain, and the lateral stripes of rhomboid expression and of other ventral neurogenic ectodermal genes. The considered principles of interaction between antagonistic gradients at the enhancer level can also be applied to diverse developmental processes, such as domain specification in imaginal discs, or even eyespot pattern formation in the butterfly wing.

The early development of the fruit fly embryo depends on an intricate but well-studied gene regulatory network. In fly eggs, maternally deposited gene products—morphogenes—form spatial concentration gradients. The graded distribution of the maternal morphogenes initiates a cascade of gene interactions leading to embryo development. Gradients of activators and repressors regulating common target genes may produce different outcomes depending on molecular mechanisms, mediating their function. Here, we describe quantitative mathematical models for the interplay between gradients of positive and negative transcriptional regulators—proteins, activating or repressing their target genes through binding the gene's regulatory DNA sequences. We predict possible spatial outcomes of the transcriptional antagonistic interactions in fly development and consider examples where the predicted cases may take place.