Master equation simulation analysis of immunostained Bicoid morphogen gradient

Background  

The concentration gradient of Bicoid protein which determines the developmental pathways in early Drosophila embryo is the best characterized morphogen gradient at the molecular level. Because different developmental fates can be elicited by different concentrations of Bicoid, it is important to probe the limits of this specification by analyzing intrinsic fluctuations of the Bicoid gradient arising from small molecular number. Stochastic simulations can be applied to further the understanding of the dynamics of Bicoid morphogen gradient formation at the molecular number level, and determine the source of the nucleus-to-nucleus expression variation (noise) observed in the Bicoid gradient.     

Distance measurements via the morphogen gradient of Bicoid in <Emphasis Type="Italic">Drosophila</Emphasis> embryos

Background  

Patterning along the anterior-posterior (A-P) axis in Drosophila embryos is instructed by the morphogen gradient of Bicoid (Bcd). Despite extensive studies of this morphogen, how embryo geometry may affect gradient formation and target responses has not been investigated experimentally.     

The formation of the Bicoid morphogen gradient requires protein movement from anteriorly localized mRNA

The Bicoid morphogen gradient directs the patterning of cell fates along the anterior-posterior axis of the syncytial Drosophila embryo and serves as a paradigm of morphogen-mediated patterning. The simplest models of gradient formation rely on constant protein synthesis and diffusion from anteriorly localized source mRNA, coupled with uniform protein degradation. However, currently such models cannot account for all known gradient characteristics. Recent work has proposed that bicoid mRNA spatial distribution is sufficient to produce the observed protein gradient, minimizing the role of protein transport. Here, we adapt a novel method of fluorescent in situ hybridization to quantify the global spatio-temporal dynamics of bicoid mRNA particles. We determine that >90% of all bicoid mRNA is continuously present within the anterior 20% of the embryo. bicoid mRNA distribution along the body axis remains nearly unchanged despite dynamic mRNA translocation from the embryo core to the cortex. To evaluate the impact of mRNA distribution on protein gradient dynamics, we provide detailed quantitative measurements of nuclear Bicoid levels during the formation of the protein gradient. We find that gradient establishment begins 45 minutes after fertilization and that the gradient requires about 50 minutes to reach peak levels. In numerical simulations of gradient formation, we find that incorporating the actual bicoid mRNA distribution yields a closer prediction of the observed protein dynamics compared to modeling protein production from a point source at the anterior pole. We conclude that the spatial distribution of bicoid mRNA contributes to, but cannot account for, protein gradient formation, and therefore that protein movement, either active or passive, is required for gradient formation.     

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.     

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.     

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

The Bicoid morphogen evolved approximately 150 MYA from a Hox3 duplication and is only found in higher dipterans. A major difference between dipteran species, however, is the size of the embryo, which varies up to 5-fold. Although the expression of developmental factors scale with egg length, it remains unknown how this scaling is achieved. To test whether scaling is accounted for by the properties of Bicoid, we expressed eGFP fused to the coding region of bicoid from three dipteran species in transgenic Drosophila embryos using the Drosophila bicoid cis-regulatory and mRNA localization sequences. In such embryos, we find that Lucilia sericata and Calliphora vicina Bicoid produce gradients very similar to the endogenous Drosophila gradient and much shorter than what they would have produced in their own respective species. The common shape of the Drosophila, Lucilia and Calliphora Bicoid gradients appears to be a conserved feature of the Bicoid protein. Surprisingly, despite their similar distributions, we find that Bicoid from Lucilia and Calliphora do not rescue Drosophila bicoid mutants, suggesting that that Bicoid proteins have evolved species-specific functional amino acid differences. We also found that maternal expression and anteriorly localization of proteins other than Bcd does not necessarily give rise to a gradient; eGFP produced a uniform protein distribution. However, a shallow gradient was observed using eGFP-NLS, suggesting nuclear localization may be necessary but not sufficient for gradient formation.     

A system of repressor gradients spatially organizes the boundaries of Bicoid-dependent target genes

The homeodomain (HD) protein Bicoid (Bcd) is thought to function as a gradient morphogen that positions boundaries of target genes via threshold-dependent activation mechanisms. Here, we analyze 66 Bcd-dependent regulatory elements and show that their boundaries are positioned primarily by repressive gradients that antagonize Bcd-mediated activation. A major repressor is the pair-rule protein Runt (Run), which is expressed in an opposing gradient and is necessary and sufficient for limiting Bcd-dependent activation. Evidence is presented that Run functions with the maternal repressor Capicua and the gap protein Kruppel as the principal components of a repression system that correctly orders boundaries throughout the anterior half of the embryo. These results put conceptual limits on the Bcd morphogen hypothesis and demonstrate how the Bcd gradient functions within the gene network that patterns the embryo.     

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.     

Pre-steady-state decoding of the Bicoid morphogen gradient

Morphogen gradients are established by the localized production and subsequent diffusion of signaling molecules. It is generally assumed that cell fates are induced only after morphogen profiles have reached their steady state. Yet, patterning processes during early development occur rapidly, and tissue patterning may precede the convergence of the gradient to its steady state. Here we consider the implications of pre-steady-state decoding of the Bicoid morphogen gradient for patterning of the anterior–posterior axis of the Drosophila embryo. Quantitative analysis of the shift in the expression domains of several Bicoid targets (gap genes) upon alteration of bcd dosage, as well as a temporal analysis of a reporter for Bicoid activity, suggest that a transient decoding mechanism is employed in this setting. We show that decoding the pre-steady-state morphogen profile can reduce patterning errors caused by fluctuations in the rate of morphogen production. This can explain the surprisingly small shifts in gap and pair-rule gene expression domains observed in response to alterations in bcd dosage.     

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.     

The role of regulated mRNA stability in establishing bicoid morphogen gradient in Drosophila embryonic development

The Bicoid morphogen is amongst the earliest triggers of differential spatial pattern of gene expression and subsequent cell fate determination in the embryonic development of Drosophila. This maternally deposited morphogen is thought to diffuse in the embryo, establishing a concentration gradient which is sensed by downstream genes. In most model based analyses of this process, the translation of the bicoid mRNA is thought to take place at a fixed rate from the anterior pole of the embryo and a supply of the resulting protein at a constant rate is assumed. Is this process of morphogen generation a passive one as assumed in the modelling literature so far, or would available data support an alternate hypothesis that the stability of the mRNA is regulated by active processes? We introduce a model in which the stability of the maternal mRNA is regulated by being held constant for a length of time, followed by rapid degradation. With this more realistic model of the source, we have analysed three computational models of spatial morphogen propagation along the anterior-posterior axis: (a) passive diffusion modelled as a deterministic differential equation, (b) diffusion enhanced by a cytoplasmic flow term; and (c) diffusion modelled by stochastic simulation of the corresponding chemical reactions. Parameter estimation on these models by matching to publicly available data on spatio-temporal Bicoid profiles suggests strong support for regulated stability over either a constant supply rate or one where the maternal mRNA is permitted to degrade in a passive manner.     

Stability and nuclear dynamics of the bicoid morphogen gradient

Patterning in multicellular organisms results from spatial gradients in morphogen concentration, but the dynamics of these gradients remain largely unexplored. We characterize, through in vivo optical imaging, the development and stability of the Bicoid morphogen gradient in Drosophila embryos that express a Bicoid-eGFP fusion protein. The gradient is established rapidly (approximately 1 hr after fertilization), with nuclear Bicoid concentration rising and falling during mitosis. Interphase levels result from a rapid equilibrium between Bicoid uptake and removal. Initial interphase concentration in nuclei in successive cycles is constant (+/-10%), demonstrating a form of gradient stability, but it subsequently decays by approximately 30%. Both direct photobleaching measurements and indirect estimates of Bicoid-eGFP diffusion constants (D < or = 1 microm(2)/s) provide a consistent picture of Bicoid transport on short ( approximately min) time scales but challenge traditional models of long-range gradient formation. A new model is presented emphasizing the possible role of nuclear dynamics in shaping and scaling the gradient.     

When are cellular oscillators sufficient for sequential segmentation?

Sequential segmentation during embryogenesis involves the generation of a repeated pattern along the embryo, which is concurrently undergoing axial elongation by cell division. Most mathematical models of sequential segmentation involve inherent cellular oscillators, acting as a segmentation clock. The cellular oscillation is assumed to be governed by the cell's physiological age or by its interaction with an external morphogen gradient. Here, we address the issue of when cellular oscillators alone are sufficient for predicting segmentation, and when a morphogen gradient is required. The key to resolving this issue lies in how cells determine positional information in the model - this is directly related to the distribution of cell divisions responsible for axial elongation. Mathematical models demonstrate that if axial elongation occurs through cell divisions restricted to the posterior end of the unsegmented region, a cell can obtain its positional information from its physiological age, and therefore cellular oscillators will suffice. Alternatively, if axial elongation occurs through cell divisions distributed throughout the unsegmented region, then positional information can be obtained through another mechanism, such as a morphogen gradient. Two alternative ways to establish a morphogen gradient in tissue with distributed cell divisions are presented - one with diffusion and the other without diffusion. Our model produces segment polarity and a distribution of segment size from the anterior-to-posterior ends, as observed in some systems. Furthermore, the model predicts segment deletions when there is an interruption in cell division, just as seen in heat shock experiments, as well as the growth and final shrinkage of the presomitic mesoderm during somitogenesis.     

BMP morphogen gradients in flies

Bone morphogenetic proteins (BMPs) act as morphogens to control patterning and growth in a variety of developing tissues in different species. How BMP morphogen gradients are established and interpreted in the target tissues has been extensively studied in Drosophila melanogaster. In Drosophila, Decapentaplegic (Dpp), a homologue of vertebrate BMP2/4, acts as a morphogen to control dorsal–ventral patterning of the early embryo and anterior–posterior patterning and growth of the wing imaginal disc. Despite intensive efforts over the last twenty years, how the Dpp morphogen gradient in the wing imaginal disc forms remains controversial, while gradient formation in the early embryo is well understood. In this review, we first focus on the current models of Dpp morphogen gradient formation in these two tissues, and then discuss new strategies using genome engineering and nanobodies to tackle open questions.     

Measurement and perturbation of morphogen lifetime: effects on gradient shape

Protein lifetime is of critical importance for most biological processes and plays a central role in cell signaling and embryonic development, where it impacts the absolute concentration of signaling molecules and, potentially, the shape of morphogen gradients. Early conceptual and mathematical models of gradient formation proposed that steady-state gradients are established by an equilibration between the lifetime of a morphogen and its rates of synthesis and diffusion, though whether gradients in fact reach steady state before being read out is a matter of controversy. In any case, this class of models predicts that protein lifetime is a key determinant of both the time to steady state and the spatial extent of a gradient. Using a method that employs repeated photoswitching of a fusion of the morphogen Bicoid (Bcd) and the photoconvertible fluorescent protein Dronpa, we measure and modify the lifetime of Dronpa-Bcd in living Drosophila embryos. We find that the lifetime of Bcd is dynamic, changing from 50 min before mitotic cycle 14 to 15 min during cellularization. Moreover, by measuring total quantities of Bcd over time, we find that the gradient does not reach steady state. Finally, using a nearly continuous low-level conversion to the dark state of Dronpa-Bcd to mimic the effect of increased degradation, we demonstrate that perturbation of protein lifetime changes the characteristic length of the gradient, providing direct support for a mechanism based on synthesis, diffusion, and degradation.     

Generation model of positional values as cell operation during the development of multicellular organisms

Many conventional models have used the positional information hypothesis to explain each elementary process of morphogenesis during the development of multicellular organisms. Their models assume that the steady concentration patterns of morphogens formed in an extracellular environment have an important property of positional information, so-called “robustness”. However, recent experiments reported that a steady morphogen pattern, the concentration gradient of the Bicoid protein, during early Drosophila embryonic development is not robust for embryo-to-embryo variability. These reports encourage a reconsideration of a long-standing problem in systematic cell differentiation: what is the entity of positional information for cells? And, what is the origin of the robust boundary of gene expression? To address these problems at a cellular level, in this article we pay attention to the re-generative phenomena that show another important property of positional information, “size invariance”. In view of regenerative phenomena, we propose a new mathematical model to describe the generation mechanism of a spatial pattern of positional values. In this model, the positional values are defined as the values into which differentiable cells transform a spatial pattern providing positional information. The model is mathematically described as an associative algebra composed of various terms, each of which is the multiplication of some fundamental operators under the assumption that the operators are derived from the remarkable properties of cell differentiation on an amputation surface in regenerative phenomena. We apply this model to the concentration pattern of the Bicoid protein during the anterior-posterior axis formation in Drosophila, and consider the conditions needed to establish the robust boundary of the expression of the hunchback gene.     

Drosophila embryo syncytial blastoderm cellular architecture and morphogen gradient dynamics: Is there a correlation?

During embryo development in many metazoan animals, the first differentiated cell type to form is an epithelial cell. This epithelial layer is modified by developmental cues of body axes formation to give rise to various tissues. The cells that arise are mesenchymal in nature and are a source of other tissue types. This epithelial to mesenchymal transition is used for tissue type formation and also seen in diseases such as cancer. Here we discuss recent findings on the cellular architecture formation in the Drosophila embryo and how it affects the developmental program of body axes formation. In particular these studies suggest the presence of compartments around each nucleus in a common syncytium. Despite the absence of plasma membrane boundaries, each nucleus not only has its own endoplasmic reticulum and Golgi complex but also its own compartmentalized plasma membrane domain above it. This architecture is potentially essential for morphogen gradient restriction in the syncytial Drosophila embryo. We discuss various properties of the dorso-ventral and the antero-posterior morphogen gradients in the Drosophila syncytium, which are likely to depend on the syncytial architecture of the embryo.